Correct compilation of specifications to deterministic asynchronous circuits

Powerful methods have been developed by A. martin and others wherby asynchronous circuits may be automatically constructed by starting from high-level specifications and incrementally transforming them into asynchronous circuits. In this paper we make the informal arguments for the correctness of this compilatin process mathematically rigorous. With rigorsouly justified transformations, specifications may be translated into circuits that provably meet their specification. A full proof of the correctness of the circuit compiler is given. Other results of independent interest include: the process model takes fairness of gates into account, hazard-freeness is formally defined, and all hazard-free circuits constructed solely of and, or, not gates and C elements are proven to behave deterministically to any outside observer. A novel notion of equivalence is used to justify the correctness of the compiler.

[1]  Matthias Felleisen,et al.  A Syntactic Theory of Sequential Control , 1987, Theor. Comput. Sci..

[2]  Alain J. Martin,et al.  Synthesis of Self-Timed Circuits by Program Transformation , 1987 .

[3]  David L. Dill,et al.  Trace theory for automatic hierarchical verification of speed-independent circuits , 1989, ACM distinguished dissertations.

[4]  Rocco De Nicola,et al.  Testing Equivalence for Processes , 1983, ICALP.

[5]  Rocco De Nicola,et al.  Testing Equivalences for Processes , 1984, Theor. Comput. Sci..

[6]  Frank Thomson Leighton,et al.  Trace Theory for Automatic Hierarchical Verification of Speed-Independent Circuits , 1988 .

[7]  Scott F. Smith,et al.  Provably Correct Synthesis of Asynchronous Circuits , 1992, Designing Correct Circuits.

[8]  Randal E. Bryant,et al.  On the Complexity of VLSI Implementations and Graph Representations of Boolean Functions with Application to Integer Multiplication , 1991, IEEE Trans. Computers.

[9]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[10]  Kees van Berkel,et al.  Handshake Circuits: An Asynchronous Architecture for VLSI Programming , 1993 .

[11]  Marly Roncken,et al.  The VLSI-programming language Tangram and its translation into handshake circuits , 1991, Proceedings of the European Conference on Design Automation..

[12]  Jan A. Bergstra,et al.  Process Algebra for Synchronous Communication , 1984, Inf. Control..

[13]  Matthew Hennessy,et al.  Algebraic theory of processes , 1988, MIT Press series in the foundations of computing.

[14]  Alain J. Martin.  Programming in VLSI: from communicating processes to delay-insensitive circuits , 1991 .

[15]  Erik Brunvand,et al.  Translating concurrent programs into delay-insensitive circuits , 1989, 1989 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers.

[16]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[17]  Van Berkel.  VLSI programming and silicon compilation , 1988 .

[18]  G.D. Plotkin,et al.  LCF Considered as a Programming Language , 1977, Theor. Comput. Sci..

[19]  Alain J. Martin.  The Design of a Self-timed Circuit for Distributed Mutual Exclusion , 1983 .

[20]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[21]  Steven M. Burns.  Automated Compilation of Concurrent Programs into Self-Timed Circuits , 1988 .

[22]  Steven M. Burns,et al.  The design of an asynchronous microprocessor , 1989, CARN.

[23]  Alain J. Martin.  Synthesis of Asynchronous VLSI Circuits , 1991 .

[24]  Alain J. Martin.  The limitations to delay-insensitivity in asynchronous circuits , 1990 .

[25]  Kees van Berkel.  Beware the isochronic fork , 1992, Integr..

[26]  Scott F. Smith,et al.  Correct Compilation of Specifications to Deterministic Asynchronous Circuits , 1993, CHARME.

[27]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[28]  Teresa H. Y. Meng,et al.  Automatic synthesis of asynchronous circuits from high-level specifications , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[29]  Matthew Hennessy,et al.  Synchronous and Asynchronous Experiments on Processes , 1984, Inf. Control..