Foundations of logic programming
Foundations of logic programming
Notions of computation and monads
Information and Computation
False loops through resource sharing
ICCAD '92 1992 IEEE/ACM international conference proceedings on Computer-aided design
Concurrent hardware: the theory and practice of self-timed design
Concurrent hardware: the theory and practice of self-timed design
The maximum set of permissible behaviors for FSM networks
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Modeling hierarchical combinational circuits
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Information and Computation
Application of Ternary Algebra to the Study of Static Hazards
Journal of the ACM (JACM)
The Denotational Description of Programming Languages: An Introduction
The Denotational Description of Programming Languages: An Introduction
Timed Boolean Functions: A Unified Formalism for Exact Timing Analysis
Timed Boolean Functions: A Unified Formalism for Exact Timing Analysis
Hazards, Critical Races, and Metastability
IEEE Transactions on Computers
Delay Models for Verifying Speed-Dependent Asynchronous Circuits
ICCD '92 Proceedings of the 1991 IEEE International Conference on Computer Design on VLSI in Computer & Processors
Timing analysis of asynchronous circuits using timed automata
CHARME '95 Proceedings of the IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods
Efficient Analysis of Cyclic Definitions
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
The synthesis of cyclic combinational circuits
Proceedings of the 40th annual Design Automation Conference
Constructive Analysis of Cyclic Circuits
EDTC '96 Proceedings of the 1996 European conference on Design and Test
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
Formal analysis of synchronous circuits
Formal analysis of synchronous circuits
Arbitration-free synchronization
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Causality analysis of synchronous programs with delayed actions
Proceedings of the 2004 international conference on Compilers, architecture, and synthesis for embedded systems
ACSD '05 Proceedings of the Fifth International Conference on Application of Concurrency to System Design
On a Ternary Model of Gate Networks
IEEE Transactions on Computers
The analysis of cyclic circuits with Boolean satisfiability
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Synchronization and Arbitration in Digital Systems
Synchronization and Arbitration in Digital Systems
Anomalous Response Times of Input Synchronizers
IEEE Transactions on Computers
A Note on Three-Valued Logic Simulation
IEEE Transactions on Computers
Hazard detection in combinational and sequential switching circuits
IBM Journal of Research and Development
Safety Property Verification of Cyclic Synchronous Circuits
Electronic Notes in Theoretical Computer Science (ENTCS)
General theory of metastable operation
IEEE Transactions on Computers
Ternary simulation: refinement of binary functions or abstraction of real-time behaviour?
DCC'96 Proceedings of the 3rd international conference on Designing Correct Circuits
Boolean Analysis of MOS Circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Analysis of cyclic combinational circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Proceedings of the Conference on Design, Automation and Test in Europe
Synchronous digital circuits as functional programs
ACM Computing Surveys (CSUR)
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We classify gate level circuits with cycles based on their stabilization behavior. We define a formal class of combinational circuits, the constructive circuits, for which signals settle to a unique value in bounded time, for any input, under a simple conservative delay model, called the up-bounded non-inertial (UN) delay. Since circuits with combinational cycles can exhibit asynchronous behavior, such as non-determinism or metastability, it is crucial to ground their analysis in a formal delay model, which previous work in this area did not do.We prove that ternary simulation, such as the practical algorithm proposed by Malik, decides the class of constructive circuits. We prove that three-valued algebra is able to maintain correct and exact stabilization information under the UN-delay model, and thus provides an adequate electrical interpretation of Malik's algorithm, which has been missing in the literature. Previous work on combinational circuits used the upbounded inertial (UI) delay to justify ternary simulation. We show that the match is not exact and that stabilization under the UI-model, in general, cannot be decided by ternary simulation. We argue for the superiority of the UN-model for reasons of complexity, compositionality and electrical adequacy. The UN-model, in contrast to the UI-model, is consistent with the hypothesis that physical mechanisms cannot implement non-deterministic choice in bounded time.As the corner-stone of our main results we introduce UN-Logic, an axiomatic specification language for UN-delay circuits that mediates between the real-time behavior and its abstract simulation in the ternary domain. We present a symbolic simulation calculus for circuit theories expressed in UN-logic and prove it sound and complete for the UN-model. This provides, for the first time, a correctness and exactness result for the timing analysis of cyclic circuits. Our algorithm is a timed extension of Malik's pure ternary algorithm and closely related to the timed algorithm proposed by Riedel and Bruck, which however was not formally linked with real-time execution models.