By Lawrence C. Paulson (auth.), Pascal Fontaine, Christophe Ringeissen, Renate A. Schmidt (eds.)

This e-book constitutes the refereed lawsuits of the ninth overseas Symposium on Frontiers of mixing structures, FroCoS 2013, held in Nancy, France, in September 2013. The 20 revised complete papers awarded including four invited papers have been rigorously reviewed and chosen from 33 submissions. FroCoS'13 seeks to provide a typical discussion board for examine within the basic region of mixture, modularization and integration of platforms, with emphasis on logic-based ones, and in their sensible use. usual themes of curiosity contain following topics: mixtures of logics equivalent to mixed predicate, temporal, modal or epistemic logics, combos and modularity in ontologies, mix of determination, systems, of satisfiability, techniques and of constraint fixing concepts, mixtures and modularity in time period rewriting, integration of equational and different theories into deductive structures, mix of deduction structures and laptop algebra, integration of knowledge constructions into constraint common sense programming and deduction, and modularizing courses and specifications.

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Extra info for Frontiers of Combining Systems: 9th International Symposium, FroCoS 2013, Nancy, France, September 18-20, 2013. Proceedings

Example text

1. The paper is structured as follows: Section 2 recalls the background notions about Presburger arithmetic and extensions. In order to identify the classes of relations whose acceleration we want to study, we are guided by software model checking applications. To this end, we provide in Section 3 a classification of the guarded assignments we are interested in. Section 4 demonstrates the practical application of the theoretical results. In particular, it presents a backward reachability procedure and shows how to incorporate acceleration with monotonic abstraction in it.

Now, let’s prove the theorem: ∀n ∈ N ∀a1 , . . , an a1 × a2 × · · · × an = an × an−1 × · · · × a1 (1) We show the corresponding input file: formulas(sos). = q(x). p(0)=1. q(0)=1. p(s(x)) = p(x)*a(x). q(s(x)) = a(x)*q(x). *(x,1)=x. *(1,x)=x. = v. x*y = y*x. end_of_list. Our tool has almost the same input format than Prover9, we just have to add the constraints to the clauses, a constraint of the form n t (where t is a term of sort nat) is written N (t) and attached to the clause as a literal. The first clause of the input file corresponds to [p(x) q(x) | n x], which is also the negation of (1), p(x) and q(x) encode the terms a1 × .

As an example with m > 1, we can take u := x1 + x2 , x2 and get u∗1 (x1 , x2 , y) = x1 + y ∗ x2 , u∗2 (x1 , x2 , y) = x2 . Here a selector is for instance 7 + x1 , ι(x1 , x2 , z) := (z − x1 − ¯ 7)//x2 . κ1 (x1 , x2 ) := ¯ 6 Accelerating Local Ground Assignments Back to our program P = (v, lI , lE , T ), we look for conditions on transitions from T allowing to accelerate them via a Σ20 -assignment. Given an iterator u(x), a selector assignment for a := a1 , . . , as (relative to u) is a tuple of selectors κ := κ1 , .

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