160,346 research outputs found
Symmetry-breaking Answer Set Solving
In the context of Answer Set Programming, this paper investigates
symmetry-breaking to eliminate symmetric parts of the search space and,
thereby, simplify the solution process. We propose a reduction of disjunctive
logic programs to a coloured digraph such that permutational symmetries can be
constructed from graph automorphisms. Symmetries are then broken by introducing
symmetry-breaking constraints. For this purpose, we formulate a preprocessor
that integrates a graph automorphism system. Experiments demonstrate its
computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other
Computing Paradig
Conflict Detection for Edits on Extended Feature Models using Symbolic Graph Transformation
Feature models are used to specify variability of user-configurable systems
as appearing, e.g., in software product lines. Software product lines are
supposed to be long-living and, therefore, have to continuously evolve over
time to meet ever-changing requirements. Evolution imposes changes to feature
models in terms of edit operations. Ensuring consistency of concurrent edits
requires appropriate conflict detection techniques. However, recent approaches
fail to handle crucial subtleties of extended feature models, namely
constraints mixing feature-tree patterns with first-order logic formulas over
non-Boolean feature attributes with potentially infinite value domains. In this
paper, we propose a novel conflict detection approach based on symbolic graph
transformation to facilitate concurrent edits on extended feature models. We
describe extended feature models formally with symbolic graphs and edit
operations with symbolic graph transformation rules combining graph patterns
with first-order logic formulas. The approach is implemented by combining
eMoflon with an SMT solver, and evaluated with respect to applicability.Comment: In Proceedings FMSPLE 2016, arXiv:1603.0857
Speeding up the constraint-based method in difference logic
"The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-40970-2_18"Over the years the constraint-based method has been successfully applied to a wide range of problems in program analysis, from invariant generation to termination and non-termination proving. Quite often the semantics of the program under study as well as the properties to be generated belong to difference logic, i.e., the fragment of linear arithmetic where atoms are inequalities of the form u v = k. However, so far constraint-based techniques have not exploited this fact: in general, Farkas’ Lemma is used to produce the constraints over template unknowns, which leads to non-linear SMT problems. Based on classical results of graph theory, in this paper we propose new encodings for generating these constraints when program semantics and templates belong to difference logic. Thanks to this approach, instead of a heavyweight non-linear arithmetic solver, a much cheaper SMT solver for difference logic or linear integer arithmetic can be employed for solving the resulting constraints. We present encouraging experimental results that show the high impact of the proposed techniques on the performance of the VeryMax verification systemPeer ReviewedPostprint (author's final draft
Schaefer's theorem for graphs
Schaefer's theorem is a complexity classification result for so-called
Boolean constraint satisfaction problems: it states that every Boolean
constraint satisfaction problem is either contained in one out of six classes
and can be solved in polynomial time, or is NP-complete.
We present an analog of this dichotomy result for the propositional logic of
graphs instead of Boolean logic. In this generalization of Schaefer's result,
the input consists of a set W of variables and a conjunction \Phi\ of
statements ("constraints") about these variables in the language of graphs,
where each statement is taken from a fixed finite set \Psi\ of allowed
quantifier-free first-order formulas; the question is whether \Phi\ is
satisfiable in a graph.
We prove that either \Psi\ is contained in one out of 17 classes of graph
formulas and the corresponding problem can be solved in polynomial time, or the
problem is NP-complete. This is achieved by a universal-algebraic approach,
which in turn allows us to use structural Ramsey theory. To apply the
universal-algebraic approach, we formulate the computational problems under
consideration as constraint satisfaction problems (CSPs) whose templates are
first-order definable in the countably infinite random graph. Our method to
classify the computational complexity of those CSPs is based on a
Ramsey-theoretic analysis of functions acting on the random graph, and we
develop general tools suitable for such an analysis which are of independent
mathematical interest.Comment: 54 page
Adding Logical Operators to Tree Pattern Queries on Graph-Structured Data
As data are increasingly modeled as graphs for expressing complex
relationships, the tree pattern query on graph-structured data becomes an
important type of queries in real-world applications. Most practical query
languages, such as XQuery and SPARQL, support logical expressions using
logical-AND/OR/NOT operators to define structural constraints of tree patterns.
In this paper, (1) we propose generalized tree pattern queries (GTPQs) over
graph-structured data, which fully support propositional logic of structural
constraints. (2) We make a thorough study of fundamental problems including
satisfiability, containment and minimization, and analyze the computational
complexity and the decision procedures of these problems. (3) We propose a
compact graph representation of intermediate results and a pruning approach to
reduce the size of intermediate results and the number of join operations --
two factors that often impair the efficiency of traditional algorithms for
evaluating tree pattern queries. (4) We present an efficient algorithm for
evaluating GTPQs using 3-hop as the underlying reachability index. (5)
Experiments on both real-life and synthetic data sets demonstrate the
effectiveness and efficiency of our algorithm, from several times to orders of
magnitude faster than state-of-the-art algorithms in terms of evaluation time,
even for traditional tree pattern queries with only conjunctive operations.Comment: 16 page
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