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Model Expansion and the Expressiveness of FO(ID) and Other Logics
"... Model expansion problem is a question of determining, given a formula and a structure for a part of the vocabulary of the formula, whether there is an expansion of this structure that satisfies the formula. Recent development of a problemsolving paradigm based on model expansion by (Mitchell & Tern ..."
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Model expansion problem is a question of determining, given a formula and a structure for a part of the vocabulary of the formula, whether there is an expansion of this structure that satisfies the formula. Recent development of a problemsolving paradigm based on model expansion by (Mitchell & Ternovska, 2005; Mitchell, Ternovska, Hach, & Mohebali, 2006) posed the question of complexity of this problem for logics used in the paradigm. We discuss the complexity of the model expansion problem for a number of logics, alongside that of satisfiability and model checking. As the task is equivalent to witnessing leading existential secondorder quantifiers in a model checking setting, the paper is in large part a survey of this area together with some new results. In particular, we describe the combined and data complexity of model expansion for FO(ID) (Denecker & Ternovska, 2008), as well as guarded and kguarded logics of (Andréka, van Benthem, & Németi, 1998) and (Gottlob, Leone, & Scarcello, 2001).
Declarative Programming of Search Problems with Builtin Arithmetic
"... We address the problem of providing a logical formalization of arithmetic in declarative modelling languages for NP search problems. The challenge is to simultaneously allow quantification over an infinite domain such as the natural numbers, provide natural modelling facilities, and control expressi ..."
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We address the problem of providing a logical formalization of arithmetic in declarative modelling languages for NP search problems. The challenge is to simultaneously allow quantification over an infinite domain such as the natural numbers, provide natural modelling facilities, and control expressive power of the language. To address the problem, we introduce an extension of the model expansion (MX) based framework to finite structures embedded in an infinite secondary structure, together with “doubleguarded ” logics for representing MX specifications for these structures. The logics also contain multiset functions (aggregate operations). Our main result is that these logics capture the complexity class NP on “smallcost ” arithmetical structures. 1
The SAT Solver MXC, version 0.75 (2008 SAT Race Version)
, 2008
"... MXC is a complete, clauselearning SAT solver, written in C++. Development of MXC began in 2006, primarily to have an inhouse solver to support the research project described in [6, 7]. Since then, we have been keeping MXC up to date with recent developments in “industrial ” SAT solver algorithms, ..."
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MXC is a complete, clauselearning SAT solver, written in C++. Development of MXC began in 2006, primarily to have an inhouse solver to support the research project described in [6, 7]. Since then, we have been keeping MXC up to date with recent developments in “industrial ” SAT solver algorithms, and submitting to the competitions. The first released version, MXC v. 0.1 [2], was entered in the 2006 Sat Race