94 research outputs found
On Optimization Modulo Theories, MaxSMT and Sorting Networks
Optimization Modulo Theories (OMT) is an extension of SMT which allows for
finding models that optimize given objectives. (Partial weighted) MaxSMT --or
equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a
very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT
or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of
state-of-the-art MAXSAT solvers, but they are specific-purpose and not always
applicable; OMT-based approaches are general-purpose, but they suffer from
intrinsic inefficiencies on MaxSMT/OMT+PB problems.
We identify a major source of such inefficiencies, and we address it by
enhancing OMT by means of bidirectional sorting networks. We implemented this
idea on top of the OptiMathSAT OMT solver. We run an extensive empirical
evaluation on a variety of problems, comparing MaxSAT-based and OMT-based
techniques, with and without sorting networks, implemented on top of
OptiMathSAT and {\nu}Z. The results support the effectiveness of this idea, and
provide interesting insights about the different approaches.Comment: 17 pages, submitted at Tacas 1
Pushing the envelope of Optimization Modulo Theories with Linear-Arithmetic Cost Functions
In the last decade we have witnessed an impressive progress in the
expressiveness and efficiency of Satisfiability Modulo Theories (SMT) solving
techniques. This has brought previously-intractable problems at the reach of
state-of-the-art SMT solvers, in particular in the domain of SW and HW
verification. Many SMT-encodable problems of interest, however, require also
the capability of finding models that are optimal wrt. some cost functions. In
previous work, namely "Optimization Modulo Theory with Linear Rational Cost
Functions -- OMT(LAR U T )", we have leveraged SMT solving to handle the
minimization of cost functions on linear arithmetic over the rationals, by
means of a combination of SMT and LP minimization techniques. In this paper we
push the envelope of our OMT approach along three directions: first, we extend
it to work also with linear arithmetic on the mixed integer/rational domain, by
means of a combination of SMT, LP and ILP minimization techniques; second, we
develop a multi-objective version of OMT, so that to handle many cost functions
simultaneously; third, we develop an incremental version of OMT, so that to
exploit the incrementality of some OMT-encodable problems. An empirical
evaluation performed on OMT-encoded verification problems demonstrates the
usefulness and efficiency of these extensions.Comment: A slightly-shorter version of this paper is published at TACAS 2015
conferenc
Unifying Reasoning and Core-Guided Search for Maximum Satisfiability
A central algorithmic paradigm in maximum satisfiability solving geared towards real-world optimization problems is the core-guided approach. Furthermore, recent progress on preprocessing techniques is bringing in additional reasoning techniques to MaxSAT solving. Towards realizing their combined potential, understanding formal underpinnings of interleavings of preprocessing-style reasoning and core-guided algorithms is important. It turns out that earlier proposed notions for establishing correctness of core-guided algorithms and preprocessing, respectively, are not enough for capturing correctness of interleavings of the techniques. We provide an in-depth analysis of these and related MaxSAT instance transformations, and propose correction set reducibility as a notion that captures inprocessing MaxSAT solving within a state-transition style abstract MaxSAT solving framework. Furthermore, we establish a general theorem of correctness for applications of SAT-based preprocessing techniques in MaxSAT. The results pave way for generic techniques for arguing about the formal correctness of MaxSAT algorithms.Peer reviewe
Incremental Cardinality Constraints for MaxSAT
Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean
Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a
succession of SAT solver calls to reach an optimum solution making extensive
use of cardinality constraints. Many of these algorithms are non-incremental in
nature, i.e. at each iteration the formula is rebuilt and no knowledge is
reused from one iteration to another. In this paper, we exploit the knowledge
acquired across iterations using novel schemes to use cardinality constraints
in an incremental fashion. We integrate these schemes with several MaxSAT
algorithms. Our experimental results show a significant performance boost for
these algo- rithms as compared to their non-incremental counterparts. These
results suggest that incremental cardinality constraints could be beneficial
for other constraint solving domains.Comment: 18 pages, 4 figures, 1 table. Final version published in Principles
and Practice of Constraint Programming (CP) 201
Optimization Modulo Theories with Linear Rational Costs
In the contexts of automated reasoning (AR) and formal verification (FV),
important decision problems are effectively encoded into Satisfiability Modulo
Theories (SMT). In the last decade efficient SMT solvers have been developed
for several theories of practical interest (e.g., linear arithmetic, arrays,
bit-vectors). Surprisingly, little work has been done to extend SMT to deal
with optimization problems; in particular, we are not aware of any previous
work on SMT solvers able to produce solutions which minimize cost functions
over arithmetical variables. This is unfortunate, since some problems of
interest require this functionality.
In the work described in this paper we start filling this gap. We present and
discuss two general procedures for leveraging SMT to handle the minimization of
linear rational cost functions, combining SMT with standard minimization
techniques. We have implemented the procedures within the MathSAT SMT solver.
Due to the absence of competitors in the AR, FV and SMT domains, we have
experimentally evaluated our implementation against state-of-the-art tools for
the domain of linear generalized disjunctive programming (LGDP), which is
closest in spirit to our domain, on sets of problems which have been previously
proposed as benchmarks for the latter tools. The results show that our tool is
very competitive with, and often outperforms, these tools on these problems,
clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic,
currently under revision. arXiv admin note: text overlap with arXiv:1202.140
The JKind Model Checker
JKind is an open-source industrial model checker developed by Rockwell
Collins and the University of Minnesota. JKind uses multiple parallel engines
to prove or falsify safety properties of infinite state models. It is portable,
easy to install, performance competitive with other state-of-the-art model
checkers, and has features designed to improve the results presented to users:
inductive validity cores for proofs and counterexample smoothing for test-case
generation. It serves as the back-end for various industrial applications.Comment: CAV 201
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