63 research outputs found
Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design â FMCAD 2022
The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing
Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design â FMCAD 2022
The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing
Combined decision procedures for nonlinear arithmetics, real and complex
We describe contributions to algorithmic proof techniques for deciding the satisfiability
of boolean combinations of many-variable nonlinear polynomial equations and
inequalities over the real and complex numbers.
In the first half, we present an abstract theory of Grobner basis construction algorithms
for algebraically closed fields of characteristic zero and use it to introduce
and prove the correctness of Grobner basis methods tailored to the needs of modern
satisfiability modulo theories (SMT) solvers. In the process, we use the technique of
proof orders to derive a generalisation of S-polynomial superfluousness in terms of
transfinite induction along an ordinal parameterised by a monomial order. We use this
generalisation to prove the abstract (âstrategy-independentâ) admissibility of a number
of superfluous S-polynomial criteria important for efficient basis construction. Finally,
we consider local notions of proof minimality for weak Nullstellensatz proofs and give
ideal-theoretic methods for computing complex âunsatisfiable coresâ which contribute
to efficient SMT solving in the context of nonlinear complex arithmetic.
In the second half, we consider the problem of effectively combining a heterogeneous
collection of decision techniques for fragments of the existential theory of real
closed fields. We propose and investigate a number of novel combined decision methods
and implement them in our proof tool RAHD (Real Algebra in High Dimensions).
We build a hierarchy of increasingly powerful combined decision methods, culminating
in a generalisation of partial cylindrical algebraic decomposition (CAD) which we
call Abstract Partial CAD. This generalisation incorporates the use of arbitrary sound
but possibly incomplete proof procedures for the existential theory of real closed fields
as first-class functional parameters for âshort-circuitingâ expensive computations during
the lifting phase of CAD. Identifying these proof procedure parameters formally
with RAHD proof strategies, we implement the method in RAHD for the case of
full-dimensional cell decompositions and investigate its efficacy with respect to the
Brown-McCallum projection operator.
We end with some wishes for the future
Computer Aided Verification
The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic
Computer Aided Verification
This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency
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