2,906 research outputs found
Recursive Online Enumeration of All Minimal Unsatisfiable Subsets
In various areas of computer science, we deal with a set of constraints to be
satisfied. If the constraints cannot be satisfied simultaneously, it is
desirable to identify the core problems among them. Such cores are called
minimal unsatisfiable subsets (MUSes). The more MUSes are identified, the more
information about the conflicts among the constraints is obtained. However, a
full enumeration of all MUSes is in general intractable due to the large number
(even exponential) of possible conflicts. Moreover, to identify MUSes
algorithms must test sets of constraints for their simultaneous satisfiabilty.
The type of the test depends on the application domains. The complexity of
tests can be extremely high especially for domains like temporal logics, model
checking, or SMT. In this paper, we propose a recursive algorithm that
identifies MUSes in an online manner (i.e., one by one) and can be terminated
at any time. The key feature of our algorithm is that it minimizes the number
of satisfiability tests and thus speeds up the computation. The algorithm is
applicable to an arbitrary constraint domain and its effectiveness demonstrates
itself especially in domains with expensive satisfiability checks. We benchmark
our algorithm against state of the art algorithm on Boolean and SMT constraint
domains and demonstrate that our algorithm really requires less satisfiability
tests and consequently finds more MUSes in given time limits
NMUS: Structural Analysis for Improving the Derivation of All MUSes in Overconstrained Numeric CSPs
Models are used in science and engineering for experimentation,
analysis, model-based diagnosis, design and planning/sheduling
applications. Many of these models are overconstrained Numeric Constraint
Satisfaction Problems (NCSP), where the numeric constraints
could have linear or polynomial relations. In practical scenarios, it is
very useful to know which parts of the overconstrained NCSP instances
cause the unsolvability.
Although there are algorithms to find all optimal solutions for this
problem, they are computationally expensive, and hence may not be applicable
to large and real-world problems. Our objective is to improve
the performance of these algorithms for numeric domains using structural
analysis. We provide experimental results showing that the use of
the different strategies proposed leads to a substantially improved performance
and it facilitates the application of solving larger and more
realistic problems.Ministerio de Educación y Ciencia DIP2006-15476-C02-0
Integrating Conflict Driven Clause Learning to Local Search
This article introduces SatHyS (SAT HYbrid Solver), a novel hybrid approach
for propositional satisfiability. It combines local search and conflict driven
clause learning (CDCL) scheme. Each time the local search part reaches a local
minimum, the CDCL is launched. For SAT problems it behaves like a tabu list,
whereas for UNSAT ones, the CDCL part tries to focus on minimum unsatisfiable
sub-formula (MUS). Experimental results show good performances on many classes
of SAT instances from the last SAT competitions
Analyzing and Extending an Infeasibility Analysis Algorithm
Constraint satisfaction problems (CSPs) involve finding assignments to a set of variables that satisfy some mathematical constraints. Unsatisfiable constraint problems are CSPs with no solution. However, useful characteristic subsets of these problems may be extracted with algorithms such as the MARCO algorithm, which outperforms the best known algorithms in the literature. A heuristic choice in the algorithm affects how it traverses the search space to output these subsets. This work analyzes the effect of this choice and introduces three improvements to the algorithm. The first of these improvements sacrifices completeness in terms of one type of subset in order to improve the output rate of another; the second and third are variations of a local search in between iterations of the algorithm which result in improved guidance in the search space. The performance of these improvements is analyzed both individually and in combinations across a variety of benchmarks and they are shown to improve the output rate of MARCO
Tunable Online MUS/MSS Enumeration
In various areas of computer science, the problem of dealing with a set of constraints arises. If the set of constraints is unsatisfiable, one may ask for a minimal description of the reason for this unsatisifiability. Minimal unsatisfiable subsets (MUSes) and maximal satisfiable subsets (MSSes) are two kinds of such minimal descriptions. The goal of this work is the enumeration of MUSes and MSSes for a given constraint system. As such full enumeration may be intractable in general, we focus on building an online algorithm, which produces MUSes/MSSes in an on-the-fly manner as soon as they are discovered. The problem has been studied before even in its online version. However, our algorithm uses a novel approach that is able to outperform the current state-of-the art algorithms for online MUS/MSS enumeration. Moreover, the performance of our algorithm can be adjusted using tunable parameters. We evaluate the algorithm on a set of benchmarks
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
Using Small MUSes to Explain How to Solve Pen and Paper Puzzles
In this paper, we present Demystify, a general tool for creating
human-interpretable step-by-step explanations of how to solve a wide range of
pen and paper puzzles from a high-level logical description. Demystify is based
on Minimal Unsatisfiable Subsets (MUSes), which allow Demystify to solve
puzzles as a series of logical deductions by identifying which parts of the
puzzle are required to progress. This paper makes three contributions over
previous work. First, we provide a generic input language, based on the Essence
constraint language, which allows us to easily use MUSes to solve a much wider
range of pen and paper puzzles. Second, we demonstrate that the explanations
that Demystify produces match those provided by humans by comparing our results
with those provided independently by puzzle experts on a range of puzzles. We
compare Demystify to published guides for solving a range of different pen and
paper puzzles and show that by using MUSes, Demystify produces solving
strategies which closely match human-produced guides to solving those same
puzzles (on average 89% of the time). Finally, we introduce a new randomised
algorithm to find MUSes for more difficult puzzles. This algorithm is focused
on optimised search for individual small MUSes
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