Computer Science Logic: 21 International Workshop, CSL 2007, by Jacques Duparc, Thomas A. Henzinger

By Jacques Duparc, Thomas A. Henzinger

The 36 revised complete papers provided including the abstracts of 6 invited lectures have been rigorously reviewed and chosen from 116 submissions. The papers are equipped in topical sections on common sense and video games, expressiveness, video games and timber, common sense and deduction, lambda calculus, finite version thought, linear good judgment, evidence idea, and video game semantics.

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Extra info for Computer Science Logic: 21 International Workshop, CSL 2007, 16th Annual Conference of the EACSL, Lausanne, Switzerland, September 11-15, 2007, Proceedings

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NCWs cannot recognize the language of all words that have infinitely many occurrences of some letter. Indeed, DBWs cannot recognize the complement language [21]. Thus, a possible way to obtain a lower bound for the translation of NBW to NCW is to construct a language that is recognizable by an NCW, but for which an NCW needs more states than an NBW due to its inability to recognize infinitely many occurrences of a letter. One such candidate is the family of languages L1 , L2 , . . over the alphabet {a, b}, where Lk contains exactly all words that have at least k occurrences of the letter a and at least k 20 O.

The strategies πi lead to the systems E(πi ) shown on the right. Let us consider the system E(π3 ). The only solution maps every variable to 2. Thus, the improvement step leads to the system E(π4 ) for which we must compute the least solution which maps every variable to values greater than or equal to 2. This solution maps x1 to 500 and x2 to 100 and is also the least solution of E. Assume that E denotes the conjunctive system xi = ei , i = 1, . . , n and that μ is a pre-fixpoint of E. We define the set Dμ (E) of derived constraints as the smallest set of constraints of the form x ≤ e such that – xi ≤ e ∈ Dμ (E) whenever xi = ei with μ(xi ) < ∞ can be rewritten (using distributivity) into xi = e ∧ e where e does not contain ∧-operators; 1 · e ∈ Dμ (E) whenever xi ≤ c · xi + e ∈ Dμ (E) where 0 < c < 1; and – xi ≤ 1−c – xi ≤ c · e + e ∈ Dμ (E) whenever xi ≤ c · xj + e ∈ Dμ (E) and xj ≤ e ∈ Dμ (E).

185–194 (1983) 44. : Lower bounds for complementation of ω-automata via the full automata technique. , Wegener, I. ) ICALP 2006. LNCS, vol. 4052, pp. 589–600. de Abstract. We present a practical algorithm for computing exact least solutions of systems of equations over the rationals with addition, multiplication with positive constants, minimum and maximum. The algorithm is based on strategy improvement combined with solving linear programming problems for each selected strategy. We apply our technique to compute the abstract least fixpoint semantics of affine programs over the relational template constraint matrix domain [20].

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