(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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Starting from a VHDL description, we generate a \ provable file in the PVS or ACL2 theorem prover. This method has been applied \ to the proof of correctness of monitors for a temporal property \ specification language.\ \>", "Abstract"], Cell[CellGroupData[{ Cell["1. Introduction", "Section"], Cell["\<\ The design of first time correct systems on a chip (SoC) involves, \ among many other challenges, guaranteeing that the system as designed will \ behave correctly. To face increasing time pressures, a design methodology \ called \"platform-based design\" is now popular in the European semiconductor \ industry: a new SoC is built according to a generic architecture, using \ pre-existing parameterized virtual modules and processor cores, the \ simulation models of which are retrieved and interconnected, possibly using \ some adaptation interfaces. Ideally, predesigned parameterized models should \ come with a formal proof of correctness for their register transfer level \ (RTL) implementation, and with a formal mathematical model allowing to reason \ about their usage in an embedding SoC. Industrial automatic tools, including \ model checking, SAT, BDD-based equivalence, etc., solve this problem for \ fixed size modules. In contrast, these methods cannot be used on \ parameterized virtual modules, which can possibly deal with unbounded size \ models and abstract data types. More elaborate techniques, such as the use of \ inference rules to establish properties on arithmetic and symbolic data, and \ inductive reasoning, are needed. Yet, one problem remains largely unsolved: \ ensuring that the mathematical model used in reasoning faithfully exhibits \ the semantics of its corresponding simulation model. This is the main topic \ of this paper.\ \>", "Text"], Cell["\<\ We start from a RTL description, used for simulation and synthesis, \ written in the VHDL standard design language. A compiler and a simulator have \ been implemented in Mathematica by G. Al Sammane [Als05]. The symbolic \ simulation of a clocked synchronized sequential circuit is used to compute \ the state transition function and the output function of the underlying Mealy \ finite state machine, under the form of a normalized IF-THEN-ELSE expression. \ From that point, we automatically produce the mathematical formulation of the \ FSM [TBA04], either as recurrence equations, or as a set of step functions. \ Finally, the post-processing part of the tool produces the model in the input \ syntax of a theorem prover, for further reasoning on the model properties. \ Currently, we implemented the flow for ACL2 and for PVS.\ \>", "Text"], Cell[TextData[{ "The paper is structured as follows. In a first part, we give an overview \ of the overall system, and briefly describe its main modules. The second \ section concentrates on the modeling aspects: we present the recurrence \ equations and the step functions, and explain how they relate to the initial \ RTL design. The third section presents the main transformation algorithms, \ and our implementation in ", StyleBox["Mathematica", FontSlant->"Italic"], ". The last part illustrates the application of the tool to the automatic \ translation of a library of primitive modules into the input format of PVS, a \ necessary step prior to the library formal proof of correctness, which has \ indeed been achieved. We conclude on the usefulness of this approach for \ proving that \"what you verify is what you synthesize\"." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["2. Symbolic Simulation", "Section"], Cell[TextData[{ StyleBox["Theosim", FontSlant->"Italic"], " [Als05] is a prototype symbolic simulation tool developed in our research \ team by Al Sammane ", StyleBox["et al", FontSlant->"Italic"], ". In a few words, it takes as input a clock synchronized sequential \ circuit, and computes the state transition functions and output function in a \ normalized conditional format. This tool performs a static stabilization of \ combinational circuits between clock edges. This simulator defines the \ symbolic value of a signal as a function of the previous symbolic value of \ all signals of its cone of influence. \n\nThe architecture of Theosim is \ given in Figure 1. 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oooo0?ooo`120?ooo`001P3oool00`3no_h0oooo0?ooo`0V0?ooo`060000 003oool0oooo0000003oool000000P3oool00`000000oooo0?ooo`050?oo o`030?knoP3oool0oooo00`0oooo00<000000?ooo`3oool02P3oool00`3n o_h0oooo0?ooo`0=0?ooo`030?knoP3oool0oooo0><0oooo0000\ \>"], "NumberedFigure", ImageSize->{337, 62}, ImageMargins->{{0, Inherited}, {Inherited, 0}}], Cell[TextData[{ StyleBox["Input circuits", FontWeight->"Bold"], " The input circuit is described in the hardware description language VHDL. \ The principles of what follows would hold for Verilog as well. The supported \ VHDL (fully described in [Als04]) is compatible with the standard subset for \ synthesis [VHDL04], including the abstract data types, but it only \ recognizes the 1999 syntax for sequential processes. " }], "Text"], Cell[TextData[{ StyleBox["Intermediate Format ", FontWeight->"Bold"], "From the source VHDL file, a proprietary compiler extracts the defining \ expression of signals and variables for one simulation cycle (", StyleBox["i.e.", FontSlant->"Italic"], " before any stabilization). It is implemented in ", StyleBox["Mathematica", FontSlant->"Italic"], ", a complete description is given in [Als04]. It is based on the \ extraction of the syntactic tree of the source VHDL which is turned into \ the Mathematica list format. " }], "Text"], Cell[TextData[{ StyleBox["Symbolic Simulation ", FontWeight->"Bold"], "The simulator is based on the VHDL simulation algorithm: at each \ simulation cycle, the active signals are updated, and processes sensitive to \ a modified signal are resumed. This step is repeated until stabilization of \ all signals: it is a delta cycle. Since the symbolic expression of signals \ and variables is simplified and normalized, a signal is stable if its \ symbolic value and its previous value are identical." }], "Text"], Cell["\<\ This simulation algorithm is used either to do symbolic simulation \ or numerical simulation. To perform a simulation for one clock cycle, one has \ to first set the clock edge, execute one clock synchronized simulation cycle, \ followed by one or more stabilization cycles. The resulting symbolic \ expressions are the results of the transition function for each state and \ output variable of the underlying finite state machine. \ \>", "Text"], Cell[TextData[{ StyleBox["Modeling ", FontWeight->"Bold"], "The transition functions given by Theosim express the symbolic value of a \ signal ", StyleBox["s", FontSlant->"Italic"], " at a given cycle in terms of its symbolic value at the previous cycle, \ and symbolic values of the other signals at the current or previous cycle. \ Two symbols are used for each signal ", StyleBox["s", FontSlant->"Italic"], ": the symbolic value at the current cycle is denoted ", StyleBox["S", FontSlant->"Italic"], " (capitalized letters of the signal name), the symbolic value at the \ previous cycle is denoted ", StyleBox["S$", FontSlant->"Italic"], "." }], "Text"], Cell[TextData[{ StyleBox["Example ", FontWeight->"Bold"], "The VHDL text on Figure 2 is an excerpt from a primitive monitor RTL \ description that will be discussed in Section 4." }], "Text"], Cell[TextData[{ StyleBox["valid <= valid_t;\nevaluate_expr: process(clk)\nbegin\n if \ clk'event and clk='1' then\n if reset_n='0' then valid_t <= '1';\n else if \ check_en = '1' then valid_t <= expr;\n else valid_t <= '1';\n end if; end \ if;\n end if; \nend process;\t", "NumberedFigure", FontFamily->"Terminal", FontSize->10], StyleBox["\n", "NumberedFigure"] }], "NumberedFigure"], Cell[TextData[{ " The output", StyleBox[" Valid", FontSlant->"Italic"], " is combinationally connected to an internal signal ", StyleBox["Valid_t", FontSlant->"Italic"], " (first line). The rest of the code is a sequential process that computes \ ", StyleBox["Valid_t", FontSlant->"Italic"], " at each rising edge of ", StyleBox["clk", FontSlant->"Italic"], ", as a function of signals ", StyleBox["reset_n", FontSlant->"Italic"], ", ", StyleBox["check_en", FontSlant->"Italic"], " and some expression ", StyleBox["expr", FontSlant->"Italic"], ". The ", StyleBox["evaluate_expr", FontSlant->"Italic"], " process and the assignment of", StyleBox[" Valid", FontSlant->"Italic"], " are concurrent, and require two simulation iterations to stabilize at \ each rising clock edge." }], "Text"], Cell[TextData[{ "The symbolic simulation of signal ", StyleBox["Valid", FontSlant->"Italic"], " returns the following expression:\n\t", Cell[BoxData[ FormBox[ StyleBox[\(VALID = \ if[RESET_N$\ == \ 0, \ 1, if[CHECK_EN$ == 1, \ EXPR$, 1]]\), FontFamily->"Terminal", FontSize->9], TraditionalForm]]] }], "Text"], Cell["\<\ Two equivalent models can be generated from the transition \ functions: a global simulation step function for the finite state machine, or \ individual functions for each state element of the machine. Which one should \ be preferred is application specific. \ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["3. Modeling functions", "Section"], Cell[CellGroupData[{ Cell["3.1. Generation of a global simulation function", "Subsection"], Cell[TextData[{ "The first solution is to model the finite state machine by means of a \ recursive function. \n\n", StyleBox["Step function ", FontWeight->"Bold"], "For each signal ", StyleBox["X", FontSlant->"Italic"], " we define a function ", StyleBox["step", FontSlant->"Italic"], " from the set of states (", StyleBox[" i.e.", FontSlant->"Italic"], " the set of value of all signals) to itself that computes the new state \ after one clock cycle. It consists in computing the image of each signal by \ the transition function." }], "Text"], Cell[BoxData[ RowBox[{ StyleBox[" ", FontSlant->"Italic"], RowBox[{ RowBox[{ StyleBox["step", FontSlant->"Italic"], ":", " ", \(S\ \[LongRightArrow]S\)}], "\[IndentingNewLine]", " ", \(s\ \[RightTeeArrow] \ s'\)}]}]], "DisplayFormula"], Cell[TextData[{ StyleBox["Example ", FontWeight->"Bold"], "Coming back to the previous example, let us denote ", Cell[BoxData[ FormBox[ SubscriptBox["D", StyleBox["valid", FontSlant->"Italic"]], TraditionalForm]]], " (resp. ", Cell[BoxData[ FormBox[ SubscriptBox["D", StyleBox["check_en", FontSlant->"Italic"]], TraditionalForm]]], ", ", Cell[BoxData[ FormBox[ SubscriptBox["D", StyleBox["valid_t", FontSlant->"Italic"]], TraditionalForm]]], ", ", Cell[BoxData[ FormBox[ SubscriptBox["D", StyleBox[ RowBox[{ StyleBox["Reset_", FontSlant->"Italic"], "t"}]]], TraditionalForm]]], ", ", Cell[BoxData[ FormBox[ SubscriptBox["D", StyleBox["expr", FontSlant->"Italic"]], TraditionalForm]]], ") the set of values of ", StyleBox["valid", FontSlant->"Italic"], " (resp. ", StyleBox["check_en, Valid_t, Reset_t, expr", FontSlant->"Italic"], "). The set of states ", StyleBox["S", FontSlant->"Italic"], " is defined by \t\t\t\t" }], "Text"], Cell[BoxData[ FormBox[ RowBox[{"S", "=", RowBox[{ SubscriptBox["D", StyleBox["valid", FontSlant->"Italic"]], "\[Times]", FormBox[ SubscriptBox["D", StyleBox["check_en", FontSlant->"Italic"]], "TraditionalForm"], "\[Times]", FormBox[ SubscriptBox["D", StyleBox["valid_t", FontSlant->"Italic"]], "TraditionalForm"], "\[Times]", FormBox[ SubscriptBox["D", StyleBox[ RowBox[{ StyleBox["Reset_", FontSlant->"Italic"], "t"}]]], "TraditionalForm"], "\[Times]", FormBox[ SubscriptBox["D", StyleBox["expr", FontSlant->"Italic"]], "TraditionalForm"]}]}], TraditionalForm]], "DisplayFormula"], Cell[TextData[{ "\nand the ", StyleBox["step", FontSlant->"Italic"], " function is defined by:" }], "Text"], Cell[BoxData[ RowBox[{ StyleBox[" ", FontSlant->"Italic"], RowBox[{ RowBox[{ StyleBox["step", FontSlant->"Italic"], ":", " ", \(S\ \ \[LongRightArrow]\ S\)}], "\[IndentingNewLine]", " ", \(v, c, vt, r, e\ \ \[RightTeeArrow] \ v', c', v', r', e'\)}]}]], "DisplayFormula"], Cell[TextData[{ "where ", StyleBox["v'", FontSlant->"Italic"], " is given by the transition function of ", StyleBox["valid", FontSlant->"Italic"], " (rewritten from ", Cell[BoxData[ \(TraditionalForm\`Valid\)], FontSlant->"Italic"], StyleBox["_t", FontSlant->"Italic"], ") ( ", StyleBox["i.e. ", FontSlant->"Italic"], "if ", StyleBox["r=0", FontSlant->"Italic"], " then ", StyleBox["1", FontSlant->"Italic"], " else if ", StyleBox["c=1", FontSlant->"Italic"], " then ", StyleBox["e", FontSlant->"Italic"], " else", StyleBox[" 1", FontSlant->"Italic"], "), ", StyleBox["c' ", FontSlant->"Italic"], " by the transition function of ", StyleBox["check_en", FontSlant->"Italic"], ", and", StyleBox[" e' ", FontSlant->"Italic"], "and ", StyleBox["r'", FontSlant->"Italic"], " are the new values of input signals ", StyleBox["expr", FontSlant->"Italic"], " and ", StyleBox["reset", FontSlant->"Italic"], "." }], "Text"], Cell[TextData[{ StyleBox["Simulation function ", FontWeight->"Bold"], "Then to compute the state after ", StyleBox["n", FontSlant->"Italic"], " cycles, a function ", StyleBox["run ", FontSlant->"Italic"], "is defined. " }], "Text"], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{" ", StyleBox[" ", FontSlant->"Italic"]}]], RowBox[{ RowBox[{ StyleBox["run", FontSlant->"Italic"], ":", " ", \(\[DoubleStruckCapitalN]\[Times] S\ \ \ \[LongRightArrow]\ S\)}], "\[IndentingNewLine]", "\t ", RowBox[{"n", ",", RowBox[{ RowBox[{"s", " ", "\[RightTeeArrow]", " ", RowBox[{ StyleBox["if", FontFamily->"Times New Roman"], " ", "n"}]}], "=", RowBox[{"0", " ", StyleBox["then", FontFamily->"Times New Roman"], " ", "s"}]}]}], "\[IndentingNewLine]", StyleBox[ RowBox[{"\t\t\t ", StyleBox[" ", FontFamily->"Times New Roman"]}]], RowBox[{ StyleBox["else", FontFamily->"Times New Roman"], " ", "run", \((n - 1, step \((s)\))\)}]}]}]], "DisplayFormula"], Cell["\<\ All signals are run concurrently.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["3.2. Generation of individual signal functions", "Subsection"], Cell["\<\ The other solution is to run signals independently. We could use a \ similar modeling technique, where the ``step'' and ``run'' functions would \ be defined for each signal, but this would be clumsy. Instead, we model \ signals by functions both in their structural and temporal dimensions, and we \ get recurrence equations. With this modeling, we can use different results on \ the formal verification of recurrence equation with affine dependencies \ especially when the dependencies are uniform and the domains of temporal and \ spatial indices have a polyhedral shape [CM04, BFR01].\ \>", "Text"], Cell[TextData[{ "In this model, the value of a signal ", StyleBox["X", FontSlant->"Italic"], " at the current cycle ", StyleBox["t", FontSlant->"Italic"], " is modeled by ", StyleBox["X(t)", FontSlant->"Italic"], " and its value one cycle before is modeled by ", StyleBox["X(t-1)", FontSlant->"Italic"], ". " }], "Text"], Cell[TextData[{ "\n\n\nAs an example, Figure 3 gives the representation in PVS [SOR01] of \ the signal ", StyleBox["Valid", FontSlant->"Italic"], " defined in Figure 2." }], "Text"], Cell[TextData[{ "\n", StyleBox[" ", FontFamily->"Terminal", FontSize->10], StyleBox["VALID(t:nat): boolean =\n (IF t=0 THEN TRUE\n ELSE IF NOT \ RESET_N_(t-1) THEN True\n ELSE IF CHECK_EN(t-1) THEN EXPR_(t-1)\n ELSE True\n\ ENDIF ENDIF ENDIF)", "NumberedFigure", FontFamily->"Terminal", FontSize->10], StyleBox["\n ", FontFamily->"Terminal", FontSize->10] }], "NumberedFigure"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["4. Implementation", "Section"], Cell["\<\ The transition functions given by Theosim are represented by their \ syntax tree and implemented by Mathematica lists. Our tool takes as input the \ list of signals and variables declared in the whole system, the desired \ representation (global or individual modeling of transition functions) and \ the language of a target theorem prover (PVS [SOR01] or ACL2 [KPM00]). The \ output is a PVS or ACL2 file specifying the system.\ \>", "Text"], Cell[TextData[{ "Our tool is composed of three main functions: ", StyleBox["parseTree", FontFamily->"Lucidatypewriter"], ", ", StyleBox["sortSignals", FontFamily->"Lucidatypewriter"], " and ", StyleBox["fileBuilding", FontFamily->"Lucidatypewriter"], "." }], "Text"], Cell[CellGroupData[{ Cell["4.1. Parsing the syntax tree", "Subsection"], Cell[TextData[{ "Function ", StyleBox["parseTree", FontFamily->"Lucidatypewriter"], " turns the syntax tree of the transition function into PVS or ACL2 \ expressions. This transformation is done according to the selected \ representation: " }], "Text"], Cell[TextData[{ StyleBox["Global modeling: ", FontWeight->"Bold"], "Signals or variables are modeled by symbol; each one of their occurrences \ in the syntax tree is directly turned into a string." }], "Text"], Cell[TextData[{ "I", StyleBox["ndividual modeling:", FontWeight->"Bold"], " Signals or variables are modeled by time functions. Their occurrences are \ turned into function calls on time ", StyleBox["t-1", FontSlant->"Italic"], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["4.2. Signals sorting", "Subsection"], Cell[TextData[{ "In ACL2 and in PVS, an object A depending on an object B must be defined \ before B. For the individual modeling, signals need to be sorted according \ to their dependency order before being written into the output file. We \ construct a directed graph, where the nodes are the signal names and the \ edges represent the dependency between signals. This graph is implemented \ using ", StyleBox["Mathematica", FontSlant->"Italic"], " facilities. To sort our signals according to their dependency, we sort \ them in a topological order with ", StyleBox["TopologicalSort", FontFamily->"Lucidatypewriter"], ". This sort does not take into account the case of mutually ", "dependent ", " signals. We first detect them in the dependency graph (with ", StyleBox["StronglyConnectedComponent", FontFamily->"Lucidatypewriter"], ") then merge them into a new sub-node representing this set of mutually \ dependent signals. The topological sort is done on this new graph. " }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["4.3. Output File definition", "Subsection"], Cell["\<\ The definition file is built according to the target language. For \ PVS, the preamble is automatically constructed (theory name, ...) and each \ symbol is typed. In ACL2 there is no preamble. Appendix A gives an excerpt of \ an automatically generated PVS file.\ \>", "Text"], Cell[TextData[{ "Global modeling: ", StyleBox[" We generate the functions ", FontWeight->"Plain"], StyleBox["step ", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["and ", FontWeight->"Plain"], StyleBox["run", FontWeight->"Plain", FontSlant->"Italic"], StyleBox[" defined in Section 3.1. according to the target language. \ Function ", FontWeight->"Plain"], " ", StyleBox["parseTree", FontFamily->"Lucidatypewriter", FontWeight->"Plain"], StyleBox[" is used to generate the PVS or ACL2 expressions.", FontWeight->"Plain"] }], "Text", FontWeight->"Bold"], Cell[TextData[{ StyleBox["Individual modeling:", FontWeight->"Bold"], " Each transition function is turned into a timed function, and written in \ the output file in the order given by ", StyleBox["sortSignals", FontFamily->"Lucidatypewriter"], ". For each inductive functions, the measure is automatically given (used \ to prove that the function is well defined), it is based on the decrease of \ time ", StyleBox["t", FontSlant->"Italic"], ". Mutually dependent signals are defined by a sub-function and a flag. In \ Appendix A, signals START_T1 and START_UNTIL are mutually dependent , they \ are defined by the sub-function START_REC. When the flag is 1, START_REC \ defines START_T1 otherwise it is START_UNTIL. For each signal the resulting \ timed function is initialized for ", StyleBox["t=0: s", FontSlant->"Italic"], "ignal initial values and types can be found automatically in the VHDL \ source syntactic tree. The type information is required in theorem provers \ like PVS, in ACL2 it is translated as a predicate on the signal domain and \ used as a precondition to enter a function body. " }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["5. Application", "Section"], Cell[TextData[{ "We developed an original method for generating hardware that monitors \ signals whose behavior is specified by logical and temporal properties under \ the form of assertions in the declarative form of the property Specification \ Language PSL. PSL is a standard specification language proposed by Accellera, \ and further standardized by IEEE [PSL]. It is based upon the Sugar 2.0 \ property specification language, and is an extension of the temporal logics \ LTL and CTL. PSL is used to describe properties that are required to hold in \ a device under verification (DUV). \n\nWe first briefly present the \ construction method and the library used to generate monitors. Then, we show \ how we use the method described in the previous section to automatically \ formalize the monitor into the logic of the PVS system, using ", StyleBox["Mathematica", FontSlant->"Italic"], ".\n" }], "Text"], Cell[CellGroupData[{ Cell["5.1. Monitor Construction", "Subsection"], Cell[TextData[{ "Our mechanism applies to any property specification language that ensures \ monotonic advancement of time, left to right through the property, such as \ the \"simple subset\" of PSL . \n\nIn the following, we use the VHDL flavor \ of PSL, but the principles apply to other syntax as well. In the text and \ the figures, 0 and 1 are used both for bits '0' and '1', and for Booleans \ False and True. \n\nMonitors (", StyleBox["cf.", FontSlant->"Italic"], " Fig 4) are built as modules that take as inputs the reset, the \ synchronization signals (clock, hand-shake, etc.) and the signals of the DUV \ that are operands of the properties to be monitored; their outputs code the \ level of satisfaction of the properties. As complex properties may be written \ by combining more elementary properties, corresponding complex monitors are \ built from the interconnection of more elementary monitors. We thus \ distinguish between internal operators/monitors that correspond to internal \ terms/sub-property; and last-level operators/monitors that correspond to the \ overall property. Monitors generated by this method have the same structure \ as the PSL formulae, and are thus easy to understand, to debug and to reuse. \ Both the \"weak\" and the \"strong\" version of the PSL operators are \ supported." }], "Text"], Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`00I@3ooom@000005<0 oooo000L0?ooo`030?knoP3oool0oooo01l0oooo00<0o_kn0?ooo`3oool0 4`3oool00`3no_h0oooo0?ooo`0>0?ooo`030000003oool0oooo04`0oooo 00<000000?ooo`3oool0D@3oool006D0oooo00<000000?ooo`3oool0C03o ool00`000000oooo0?ooo`1A0?ooo`00903oool00`3no_h0oooo0?ooo`0; 0?ooo`030?knoP3oool0oooo01X0oooo00<0o_kn0?ooo`3oool04`3oool0 0`000000oooo0?ooo`1<0?ooo`030000003oool0oooo0540oooo000e0?oo o`030?knoP3oool0oooo01L0oooo00<0o_kn0?ooo`3oool01@3oool00`3n o_h0oooo0?ooo`0;0?ooo`030000003oool0o_kn04`0oooo00<000000?oo o`3oool0D@3oool002`0oooo00<0o_kn0?ooo`3oool02`3oool4000002L0 oooo00<000000?ooo`3oool0C03oool00`000000oooo0?ooo`1A0?ooo`00 >P3oool00`000000oooo0?ooo`02000000l0oooo00<0o_kn0?ooo`3oool0 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"NumberedFigure", ImageSize->{264, 110}, ImageMargins->{{0, Inherited}, {Inherited, 0}}], Cell[TextData[{ "The monitor outputs have the following significance: ", StyleBox["Checking", FontSlant->"Italic"], " indicates when output ", StyleBox["Valid", FontSlant->"Italic"], " is effective and ", StyleBox["Valid", FontSlant->"Italic"], " provides the evaluation result (1 means absence of error, 0 means error). \ ", StyleBox["Pending", FontSlant->"Italic"], " means that the evaluation of the property has been started, but the \ result is still unknown; ", StyleBox["Valid", FontSlant->"Italic"], " is '1' when ", StyleBox["Pending ", FontSlant->"Italic"], " is '1'. ", "Outputs ", StyleBox["Checking", FontSlant->"Italic"], " and ", StyleBox["Valid", FontSlant->"Italic"], " are generated by the last monitor. They can be used to generate \ appropriate actions when a valuation of the property has been obtained. " }], "Text"], Cell["\<\ \ \>", "Text"], Cell[TextData[{ StyleBox["Example: ", FontWeight->"Bold"], "Assume we are interested in the behavior of signals ", StyleBox["A, B, C", FontSlant->"Italic"], " in a design synchronized by the rising edges of its master clock clk. We \ want to observe that signals ", StyleBox["A, B, C", FontSlant->"Italic"], " satisfy property ", StyleBox["P", FontSlant->"Italic"], ", expressed as:" }], "Text"], Cell[TextData[StyleBox["Property P is always (A -> next_event![2](B) (C)) \ @rising_edge(clk); ", FontFamily->"Lucidatypewriter"]], "Text"], Cell[TextData[{ StyleBox["P ", FontSlant->"Italic"], "is an invariant (it must always hold), which states that whenever ", StyleBox["A", FontSlant->"Italic"], " is '1', it must be the case that the second times ", StyleBox["B", FontSlant->"Italic"], " takes the value '1', ", StyleBox["C", FontSlant->"Italic"], " takes the value '1' : " }], "Text"], Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg`0008Lc<`3omoHL 0?ooo`060?knoP3oool0ooOf0?oViP27SX0 ooWj7P3oool0103onOX0ong]07Hj>P3onOX;0?ooo`80ooom4`3oool0103o nOX0MSXj0?o]k@3onOXM0?ooo`050?koo`3on_X0ong]07Hj>P3onOX07@3o ool01@3oood0ooWh0?o]k@1f>SX0ooWj01L0oooo0P3oood70?ooo`040?oi 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observed \ on signals ", StyleBox["A, B, C", FontSlant->"Italic"], ". The vertical dotted lines represent the successive rising edges of ", StyleBox["clk", FontSlant->"Italic"], ", which have been numbered for the purpose of this explanation. ", StyleBox["Start, Checking,\nValid ", FontSlant->"Italic"], "and", StyleBox[" Pending", FontSlant->"Italic"], " are the input-outputs of the monitor for ", StyleBox["P", FontSlant->"Italic"], ", as explained above." }], "Text"], Cell[TextData[{ StyleBox["Top waveform", FontWeight->"Bold"], ": Property ", StyleBox["P", FontSlant->"Italic"], " is monitored on the trace from ", StyleBox["clk ", FontSlant->"Italic"], "edge #0 to ", StyleBox["clk", FontSlant->"Italic"], " edge #5. At ", StyleBox["clk", FontSlant->"Italic"], " edge #1, ", StyleBox["A", FontSlant->"Italic"], " takes value '1'. Thus, starting from ", StyleBox["clk ", FontSlant->"Italic"], "edge #1, property ", StyleBox["P", FontSlant->"Italic"], " holds on the trace ending at ", StyleBox["clk", FontSlant->"Italic"], " edge #5, if and only if ", StyleBox["B", FontSlant->"Italic"], " takes value '1' twice, and the second time ", StyleBox["C", FontSlant->"Italic"], " takes value '1'. ", StyleBox["P", FontSlant->"Italic"], " fails since ", StyleBox["B", FontSlant->"Italic"], " holds only once. At ", StyleBox["clk", FontSlant->"Italic"], " edge #6, the property is still pending. According to the design of our \ monitors, output ", StyleBox["Pending ", FontSlant->"Italic"], "is significant only one cycle after the end of the trace." }], "Text"], Cell[TextData[{ StyleBox["Bottom waveform", FontWeight->"Bold"], ": Property ", StyleBox["P", FontSlant->"Italic"], " is monitored on the trace from clk edge ", Cell[BoxData[ \(TraditionalForm\`#0\)]], " to clk edge #6. At clk edge #2, ", StyleBox["A", FontSlant->"Italic"], " takes value 1, and remains 1 for one clock cycle. On the waveform, ", StyleBox["P", FontSlant->"Italic"], " does not hold since the second time", StyleBox[" B", FontSlant->"Italic"], " takes value '1', ", StyleBox["C", FontSlant->"Italic"], " takes value '0' and ", StyleBox["Valid", FontSlant->"Italic"], " takes value '0' one cycle later. According to our design, output ", StyleBox["Checking", FontSlant->"Italic"], " takes value 1 at the same edge as ", StyleBox["B", FontSlant->"Italic"], " takes value '1' for the second time, and the value of output ", StyleBox["Valid", FontSlant->"Italic"], " is significant one cycle later. Note that output", StyleBox[" Pending ", FontSlant->"Italic"], "takes value '0', meaning that the property is not pending. If ", StyleBox["C", FontSlant->"Italic"], " took value '1' at clk edge #5, the value of ", StyleBox["Valid", FontSlant->"Italic"], " at ", StyleBox["clk ", FontSlant->"Italic"], " #6 would take '1' and the property would hold." }], "Text"], Cell[TextData[{ "Figure 6 shows the structural interconnection of primitive components to \ form the monitor for property ", StyleBox["P", FontSlant->"Italic"], ". 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It is the structural interconnection of primitive monitors, one for each \ temporal operator present in property ", StyleBox["P: always, impl ", FontSlant->"Italic"], "(for '\[Rule]'), ", StyleBox["next_event.", FontSlant->"Italic"], " An additional primitive module called ", StyleBox["gen_init", FontSlant->"Italic"], " starts the global monitoring process." }], "Text"], Cell[TextData[{ "\n", StyleBox["Structure of a primitive monitor:", FontWeight->"Bold"], "\nThe library monitors contains one primitive monitor for each FL operator \ of PSL. Operators that take one or two integer parameters, such as ", StyleBox["next", FontSlant->"Italic"], " or ", StyleBox["next_a", FontSlant->"Italic"], ", have corresponding generic monitors with the same parameters. All \ primitive monitors were designed according to a common basic structure of two \ main blocks. The first one, the ", StyleBox["Checking Window Block", FontSlant->"Italic"], " generates the temporal window for the evaluation of the operands, and \ sets an internal check enabling ", StyleBox["check_en", FontSlant->"Italic"], " signal, based on the evaluation requirement (", StyleBox["Start", FontSlant->"Italic"], " input signal) and the semantics of the operator. The second one, ", StyleBox["the Evaluation Block", FontSlant->"Italic"], " executes the checking of the operands, when the checking enable signal is \ '1'. When ", StyleBox["reset", FontSlant->"Italic"], " is active, the monitor stays in its reset state. Otherwise, when ", StyleBox["check_en", FontSlant->"Italic"], " is active, the operand is checked and output", StyleBox[" Valid", FontSlant->"Italic"], " represents the result. When ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ StyleBox["check", FontSlant->"Italic"], "_"}]], TraditionalForm]]], StyleBox["en", FontSlant->"Italic"], " is inactive, execution is stopped, and output ", StyleBox["Valid ", FontSlant->"Italic"], "stays in its default value 1." }], "Text"], Cell[TextData[{ StyleBox["Construction of complex monitors by interconnection of primitive \ components :", FontWeight->"Bold"], "\nTo generate the monitors for complex properties, primitive single \ operator monitors are interconnected to construct a complex property monitor. \ The method is based on the syntax tree of the property. A node in the tree \ represents a PSL operator, a leaf represents a basic operand (signal or \ constant value), the edges connect an operator with its operands. Some \ operators have two operands, some have only one." }], "Text"], Cell["More details and example may be found in [BL05]. ", "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["5.2. Formalization", "Subsection"]], "Subsection"], Cell["\<\ The proof of correctness of both the library components and the \ interconnection method, with respect to the formal semantics of the PSL \ reference manual was done with the system. The choice of PVS was motivated \ by the fact that the PSL semantics are expressed in second-order logic and \ thus directly represented by the input formalism. 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To prove each monitor correct, we extract its finite state machine \ (FSM) model, and translate it in the input formalism. This process has been \ automated, with the help of symbolic simulation (see Section 2). Appendix A \ gives the modeling file in for the monitor ", StyleBox["until", FontSlant->"Italic"], ".\n\nSince we want to prove that the monitors implement the semantics if \ and only if some signals are active on a given number of cycles (a trace), we \ have chosen recurrence equations. Indeed, we are not interested on the whole \ state of our FSM (the monitor) at a given time but on the value of one \ signal on a whole trace. In this case, it is much easier to prove properties \ on signals modeled independently than concurrently. Furthermore, this \ modeling allowed us to benefit from the formal verification technique based \ on recurrence equations [QRMC06].\n\nThen, the PSL semantics are represented \ in PVS, and we generate automatically several theorems for each operator. All \ theorems are proved with PVS and the proof can be found in [MB05]." }], "Text"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["6. Conclusion", "Section"], Cell["\<\ In this paper, we have described and illustrated a new method to \ verify the correctness of parameterized library components. The synthesizable \ design of each component, written inVHDL, is processed by a symbolic \ simulator that computes the transition functions of all the state and output \ variables of the design. Depending on the characteristics of the problem at \ hand, the designer may choose to reason in terms of recurrence equations on \ in terms of step functions, to prove his/her design compliant to a high level \ semantic specification.\ \>", "Text"], Cell[TextData[{ "A prototype tool has been implemented. The use of the rewriting and \ fixed-point computation of ", StyleBox["Mathematica", FontSlant->"Italic"], " has been crucial to quickly validate the overall approach and program the \ core algorithms of the symbolic simulator and provable model generators." }], "Text"], Cell[TextData[{ "The main limitations to the dissemination of the tool are twofold. First, \ the user interface is currently very primitive, and requires prior knowledge \ of the ", StyleBox["Mathematica", FontSlant->"Italic"], " input syntax, which is acceptable for verification experts but not for \ hardware designers. Second, the complexity of the design that may be \ processed by the symbolic simulator is restricted by the memory space and \ allowed depth of nested expressions. As a consequence, our tool should be \ intended for use by expert formal verification engineers, who will perform, \ once and for all, the proof of correctness of library elements and modest \ size IP's to be used as building blocks for large projects." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Bibliography", "Section"], Cell[TextData[{ "[Als04] G. Al Sammane, ", StyleBox["Specification of the VHDL subset supported by TheoSim,", FontSlant->"Italic"], " Tima Laboratory, ISRN: TIMA-RR--04/07-03--FR." }], "Text"], Cell[TextData[{ "[Als05] G. Al Sammane, ", StyleBox["Simulation symbolique des circuits d\[EAcute]crits au niveau \ algorithmique", FontSlant->"Italic"], ", PhD thesis, Universit\[EAcute] Joseph Fourier, July, 2005, (in French)." }], "Text"], Cell[TextData[{ "[BL05] D. Borrione and M. Liu and P. Ostier and L. Fesquet, PSL-based \ online monitoring of digital systems, in Proc. ", StyleBox["Forum on specification & Design Languages", FontSlant->"Italic"], " (FDL'05), 2005." }], "Text"], Cell[TextData[{ "[BFR01] D. Barthou and P. Feautrier and X. Redon, ", StyleBox["On the Equivalence of Two Systems of Affine Recurrence Equations", FontSlant->"Italic"], ", RR n\[Degree] 4285, INRIA, 2001." }], "Text"], Cell[TextData[{ "[CM04] D. Cachera and K. Morin-Allory, Verification of safety properties \ for parameterized regular systems, in ", StyleBox["Trans. on Embedded Computing Sys.", FontSlant->"Italic"], ", 4:2, 2005, ACM Press ." }], "Text"], Cell[TextData[{ "[KPM00] M. Kaufmann and P. Manolios and J Strother Moore, in Proc. ", StyleBox["ACL2 Computer Aided Reasoning: An Approach", FontSlant->"Italic"], ", Kluwer Academic Press, 2000." }], "Text"], Cell[TextData[{ "[MB05] K. Morin-Allory and D. Borrione, A proof of correctness for the \ construction of property monitors, in Proc. ", StyleBox["High Level Design Validation and Test (HLDVT'05)", FontSlant->"Italic"], ", Dec., 2005, IEEE Press." }], "Text"], Cell[TextData[{ "[QRMC06] P. Quinton and T. Risset and K. Morin-Allory and D. Cachera, \ Designing Parallel Programs and Integrated Circuit, in Proc. ", StyleBox["International Mathematica Symposium", FontSlant->"Italic"], ", Avignon, 2006." }], "Text"], Cell[TextData[{ "[PSL] ", StyleBox["1850 IEEE Standard for Property Specification Language", FontSlant->"Italic"], ", IEEE, October, 2005." }], "Text"], Cell[TextData[{ "[SOR01] N. Shankar and S. Owre and J.M. Rushby and D.W.J. \ Stringer-Calvert, ", StyleBox["Prover Guide", FontSlant->"Italic"], ", 2001, Computer Science Laboratory, SRI International." }], "Text"], Cell[TextData[{ "[TBA04] D. Toma and D. Borrione and G. Al Sammane, Combining Several \ Paradigms for Circuit Validation and Verification, in Proc. ", StyleBox["CASSIS 2004", FontSlant->"Italic"], ", 2005, vol. 3362, LNCS, Springer." }], "Text"], Cell[TextData[{ "[VHDL04] ", StyleBox["1076.6-2004 IEEE Standard for VHDL Register Transfer Level (RTL) \ Synthesis", FontSlant->"Italic"], ", IEEE, 2004.\n" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Appendix A", "Section"], Cell["\<\ mnt_until_monitor : THEORY BEGIN % ASSUMING % assuming declarations weak_excl_op_1 : nat=0; strong_excl_op_1 : nat=1; weak_incl_op_1 : nat=2; strong_incl_op_1 : nat=3; op_type_1 : nat =weak_excl_op_1; % ENDASSUMING % VHDL DEFINITIONS PENDING_T(t:nat):RECURSIVE boolean= (IF t=0 THEN FALSE ELSE IF (RESET_N(t-1) = False) THEN False ELSE IF (COND1(t-1) = True) THEN False ELSE IF (START(t-1) = True) THEN True ELSE PENDING_T(t-1) ENDIF ENDIF ENDIF ENDIF) MEASURE t START_REC(flag:subrange(1,2),t:nat):RECURSIVE boolean= IF flag=1 THEN (...) ELSE (...) ENDIF MEASURE t START_T1(t:nat):boolean=START_REC(1,t); START_UNTIL(t:nat):boolean=START_REC(2,t); PENDING(t:nat):RECURSIVE boolean= (...) MEASURE t CHECKING(t:nat): boolean = (...) VALID(t:nat): boolean = ( ...) % END VHDL DEFINITIONS % THEOREMS (to complete) % END THEOREMS END mnt_until_monitor \ \>", "Text", FontFamily->"Lucidatypewriter"] }, Open ]] }, Open ]] }, FrontEndVersion->"5.2 for X", ScreenRectangle->{{0, 1920}, {0, 1200}}, ScreenStyleEnvironment->"Working", PrintingStyleEnvironment->"Printout", WindowToolbars->{}, WindowSize->{731, 877}, WindowMargins->{{230, Automatic}, {Automatic, 25}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PageHeaders->{{ Inherited, Inherited, Cell[ "Katell Morin-Allory, Dominique Borrione", "Header"]}, { Cell[ "Automatic generation of a provable circuit model: from VHDL to \ PVS", "Header"], Inherited, Inherited}}, PrintingOptions->{"PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "PostScriptOutputFile":>FrontEnd`FileName[{$RootDirectory, "home", "papegay", \ "ims06", "eproc", "articles"}, "MorinAllory.nb.ps", CharacterEncoding -> \ "iso8859-1"], "Magnification"->1}, Magnification->1, StyleDefinitions -> "IMS2006styles.nb" ] (******************************************************************* Cached data follows. 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