423 research outputs found
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
Solving MaxSAT and #SAT on structured CNF formulas
In this paper we propose a structural parameter of CNF formulas and use it to
identify instances of weighted MaxSAT and #SAT that can be solved in polynomial
time. Given a CNF formula we say that a set of clauses is precisely satisfiable
if there is some complete assignment satisfying these clauses only. Let the
ps-value of the formula be the number of precisely satisfiable sets of clauses.
Applying the notion of branch decompositions to CNF formulas and using ps-value
as cut function, we define the ps-width of a formula. For a formula given with
a decomposition of polynomial ps-width we show dynamic programming algorithms
solving weighted MaxSAT and #SAT in polynomial time. Combining with results of
'Belmonte and Vatshelle, Graph classes with structured neighborhoods and
algorithmic applications, Theor. Comput. Sci. 511: 54-65 (2013)' we get
polynomial-time algorithms solving weighted MaxSAT and #SAT for some classes of
structured CNF formulas. For example, we get algorithms for
formulas of clauses and variables and size , if has a linear
ordering of the variables and clauses such that for any variable occurring
in clause , if appears before then any variable between them also
occurs in , and if appears before then occurs also in any clause
between them. Note that the class of incidence graphs of such formulas do not
have bounded clique-width
Preprocessing and Stochastic Local Search in Maximum Satisfiability
Problems which ask to compute an optimal solution to its instances are called optimization problems. The maximum satisfiability (MaxSAT) problem is a well-studied combinatorial optimization problem with many applications in domains such as cancer therapy design, electronic markets, hardware debugging and routing. Many problems, including the aforementioned ones, can be encoded in MaxSAT. Thus MaxSAT serves as a general optimization paradigm and therefore advances in MaxSAT algorithms translate to advances in solving other problems.
In this thesis, we analyze the effects of MaxSAT preprocessing, the process of reformulating the input instance prior to solving, on the perceived costs of solutions during search. We show that after preprocessing most MaxSAT solvers may misinterpret the costs of non-optimal solutions. Many MaxSAT algorithms use the found non-optimal solutions in guiding the search for solutions and so the misinterpretation of costs may misguide the search.
Towards remedying this issue, we introduce and study the concept of locally minimal solutions. We show that for some of the central preprocessing techniques for MaxSAT, the perceived cost of a locally minimal solution to a preprocessed instance equals the cost of the corresponding reconstructed solution to the original instance.
We develop a stochastic local search algorithm for MaxSAT, called LMS-SLS, that is prepended with a preprocessor and that searches over locally minimal solutions. We implement LMS-SLS and analyze the performance of its different components, particularly the effects of preprocessing and computing locally minimal solutions, and also compare LMS-SLS with the state-of-the-art SLS solver SATLike for MaxSAT.
On abstraction refinement for program analyses in Datalog
A central task for a program analysis concerns how to efficiently find a program abstraction that keeps only information relevant for proving properties of interest. We present a new approach for finding such abstractions for program analyses written in Datalog. Our approach is based on counterexample-guided abstraction refinement: when a Datalog analysis run fails using an abstraction, it seeks to generalize the cause of the failure to other abstractions, and pick a new abstraction that avoids a similar failure. Our solution uses a boolean satisfiability formulation that is general, complete, and optimal: it is independent of the Datalog solver, it generalizes the failure of an abstraction to as many other abstractions as possible, and it identifies the cheapest refined abstraction to try next. We show the performance of our approach on a pointer analysis and a typestate analysis, on eight real-world Java benchmark programs
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