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This e-book constitutes the refereed complaints of the ninth overseas Symposium on Frontiers of mixing platforms, FroCoS 2013, held in Nancy, France, in September 2013. The 20 revised complete papers awarded including four invited papers have been conscientiously reviewed and chosen from 33 submissions. FroCoS'13 seeks to supply a typical discussion board for examine within the basic quarter of mix, modularization and integration of structures, with emphasis on logic-based ones, and in their useful use. ordinary subject matters of curiosity comprise following matters: mixtures of logics comparable to mixed predicate, temporal, modal or epistemic logics, mixtures and modularity in ontologies, mix of determination, methods, of satisfiability, systems and of constraint fixing recommendations, combos and modularity in time period rewriting, integration of equational and different theories into deductive platforms, blend of deduction structures and machine algebra, integration of information buildings into constraint good judgment programming and deduction, and modularizing courses and specifications.
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Extra resources for Frontiers of Combining Systems: 9th International Symposium, FroCoS 2013, Nancy, France, September 18-20, 2013. Proceedings
Sample text
To mean both that the term t or the 3 The procedure Reverse outputs to the array O the reverse of the array I; the procedure allDiff checks whether the entries of the array a are all different. Many thanks to Madhusudan Parthasarath and his group for pointing us to challenging problems with arrays of unknown length, including the allDiff example. Definability of Accelerated Relations 27 quantifier-free formula φ have free variables included in x and that the free function, free constants symbols occurring in them are among a, c.
Formally, we have u0 (x) := x and un+1 (x) := u1 (un (x)), . . , um (un (x)) . Definition 3. A tuple of terms u like (6) is said to be an iterator iff there exists an m-tuple of m + 1-ary terms u∗ (x, y) := u∗1 (x1 , . . , xm , y), . . , u∗m (x1 , . . , xm , y) such that for any natural number n it happens that the formula ¯) un (x) = u∗ (x, n (7) 6 is valid. Given an iterator u as above, we say that an m-ary term κ(x1 , . . , xm ) is a selector for u iff there is an m + 1-ary term ι(x1 , . .
LNCS (LNAI), vol. 3702, pp. 262–276. Springer, Heidelberg (2005) Definability of Accelerated Relations in a Theory of Arrays and Its Applications Francesco Alberti1 , Silvio Ghilardi2 , and Natasha Sharygina1 1 Formal Verification Lab, University of Lugano, Lugano, Switzerland 2 Universit` a degli Studi di Milano, Milan, Italy Abstract. e. transitive closures) are definable in the theory of arrays via ∃∗ ∀∗ -first order formulae. We apply this result to model checking of unbounded array programs, where the computation of such accelerations can be used to prevent divergence of reachability analysis.