By Joao Marques-Silva, Inês Lynce, Vasco Manquinho (auth.), Iliano Cervesato, Helmut Veith, Andrei Voronkov (eds.)

This booklet constitutes the refereed lawsuits of the fifteenth foreign convention on good judgment for Programming, man made Intelligence, and Reasoning, LPAR 2008, which happened in Doha, Qatar, in the course of November 22-27, 2008.

The forty five revised complete papers awarded including three invited talks have been conscientiously revised and chosen from 153 submissions. The papers deal with all present matters in computerized reasoning, computational good judgment, programming languages and their functions and are equipped in topical sections on automata, linear mathematics, verification wisdom illustration, evidence idea, quantified constraints, in addition to modal and temporal logics.

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Extra resources for Logic for Programming, Artificial Intelligence, and Reasoning: 15th International Conference, LPAR 2008, Doha, Qatar, November 22-27, 2008. Proceedings

Example text

As´ın et al. turn can cause dramatic changes in the runtime on a given instance. Therefore, most changes in SAT solvers are hard to assess, as they can only be evaluated by running a statistically significant amount of problems and measuring aspects like runtime averages. For this reason, all experiments mentioned from now on in this paper have been designed in such a way that for each method for proof/core extraction our solver performs exactly the same search (which was impossible in the algorithm with marker literals).

1. If g, v ∈ α, then g ∈ S. 2. If g ∈ S and (i) g is a non-input gate, (ii) g is justified in τ , and (iii) gi , vi ∈ σ for some subset minimal justification σ for g, τ (g) , then gi ∈ S. Notice that by this definition jcone(C α , τ ) is unambiguously defined. 34 M. J¨arvisalo, T. Junttila, and I. e. those gates in the cone that are not justified: jfront(C α , τ ) = {g ∈ jcone(C α , τ ) | g is not justified in τ }. A gate g is interesting in τ if it belongs to the frontier jfront(C α , τ ) or is a descendant of a gate in it; the set of all gates that are interesting in τ is denoted by interest(C α , τ ).

Execute the line 10 in a way that only flips the values of children of g whose values differ in τ and τ ; the value of at least one such child 1 1 is flipped. This step happens with the probability of at least |G| · p · q · 2|G| , where 1 the term 2|G| comes from the fact that a gate always has less than |G| children, and 1 thus the probability of picking the desired justification is at least 2|G| . As both steps above (i) flip the value of at least one gate to one in τ and (ii) never flip a gate whose value already is the same as in τ , they are executed at most |G| times: after this τ = τ and thus jfront(C α , τ ) = jfront(C α , τ ) = ∅.

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