142 research outputs found
Counterexample Guided Abstraction Refinement Algorithm for Propositional Circumscription
Circumscription is a representative example of a nonmonotonic reasoning
inference technique. Circumscription has often been studied for first order
theories, but its propositional version has also been the subject of extensive
research, having been shown equivalent to extended closed world assumption
(ECWA). Moreover, entailment in propositional circumscription is a well-known
example of a decision problem in the second level of the polynomial hierarchy.
This paper proposes a new Boolean Satisfiability (SAT)-based algorithm for
entailment in propositional circumscription that explores the relationship of
propositional circumscription to minimal models. The new algorithm is inspired
by ideas commonly used in SAT-based model checking, namely counterexample
guided abstraction refinement. In addition, the new algorithm is refined to
compute the theory closure for generalized close world assumption (GCWA).
Experimental results show that the new algorithm can solve problem instances
that other solutions are unable to solve
Synthesis of a simple self-stabilizing system
With the increasing importance of distributed systems as a computing
paradigm, a systematic approach to their design is needed. Although the area of
formal verification has made enormous advances towards this goal, the resulting
functionalities are limited to detecting problems in a particular design. By
means of a classical example, we illustrate a simple template-based approach to
computer-aided design of distributed systems based on leveraging the well-known
technique of bounded model checking to the synthesis setting.Comment: In Proceedings SYNT 2014, arXiv:1407.493
Skolem Functions for Factored Formulas
Given a propositional formula F(x,y), a Skolem function for x is a function
\Psi(y), such that substituting \Psi(y) for x in F gives a formula semantically
equivalent to \exists F. Automatically generating Skolem functions is of
significant interest in several applications including certified QBF solving,
finding strategies of players in games, synthesising circuits and bit-vector
programs from specifications, disjunctive decomposition of sequential circuits
etc. In many such applications, F is given as a conjunction of factors, each of
which depends on a small subset of variables. Existing algorithms for Skolem
function generation ignore any such factored form and treat F as a monolithic
function. This presents scalability hurdles in medium to large problem
instances. In this paper, we argue that exploiting the factored form of F can
give significant performance improvements in practice when computing Skolem
functions. We present a new CEGAR style algorithm for generating Skolem
functions from factored propositional formulas. In contrast to earlier work,
our algorithm neither requires a proof of QBF satisfiability nor uses
composition of monolithic conjunctions of factors. We show experimentally that
our algorithm generates smaller Skolem functions and outperforms
state-of-the-art approaches on several large benchmarks.Comment: Full version of FMCAD 2015 conference publicatio
Evaluating QBF Solvers: Quantifier Alternations Matter
We present an experimental study of the effects of quantifier alternations on
the evaluation of quantified Boolean formula (QBF) solvers. The number of
quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is
directly related to the theoretical hardness of the respective QBF
satisfiability problem in the polynomial hierarchy. We show empirically that
the performance of solvers based on different solving paradigms substantially
varies depending on the numbers of alternations in PCNFs. In related
theoretical work, quantifier alternations have become the focus of
understanding the strengths and weaknesses of various QBF proof systems
implemented in solvers. Our results motivate the development of methods to
evaluate orthogonal solving paradigms by taking quantifier alternations into
account. This is necessary to showcase the broad range of existing QBF solving
paradigms for practical QBF applications. Moreover, we highlight the potential
of combining different approaches and QBF proof systems in solvers.Comment: preprint of a paper to be published at CP 2018, LNCS, Springer,
including appendi
Understanding and Extending Incremental Determinization for 2QBF
Incremental determinization is a recently proposed algorithm for solving
quantified Boolean formulas with one quantifier alternation. In this paper, we
formalize incremental determinization as a set of inference rules to help
understand the design space of similar algorithms. We then present additional
inference rules that extend incremental determinization in two ways. The first
extension integrates the popular CEGAR principle and the second extension
allows us to analyze different cases in isolation. The experimental evaluation
demonstrates that the extensions significantly improve the performance
DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL
We present the latest major release version 6.0 of the quantified Boolean
formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of
the conflict-driven clause learning (CDCL) paradigm implemented in state of the
art propositional satisfiability (SAT) solvers. The Q-resolution calculus
(QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce
QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of
the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0
implements a variant of QCDCL which is based on a generalization of QRES. This
generalization is due to a set of additional axioms and leaves the original
Q-resolution rules unchanged. The generalization of QRES enables QCDCL to
potentially produce exponentially shorter proofs than the traditional variant.
We present an overview of the features implemented in DepQBF and report on
experimental results which demonstrate the effectiveness of generalized QRES in
QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS,
Springer, 201
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