By David Basin, Cas Cremers (auth.), Anuj Dawar, Helmut Veith (eds.)
This quantity constitutes the refereed complaints of the twenty fourth overseas Workshop on laptop technology common sense, CSL 2010, held in Brno, Czech Republic, in August 2010. The 33 complete papers offered including 7 invited talks, have been conscientiously reviewed and chosen from 103 submissions. themes coated comprise computerized deduction and interactive theorem proving, confident arithmetic and sort idea, equational good judgment and time period rewriting, automata and video games, modal and temporal common sense, version checking, selection methods, logical features of computational complexity, finite version idea, computational facts concept, common sense programming and constraints, lambda calculus and combinatory common sense, express good judgment and topological semantics, area thought, database conception, specification, extraction and transformation of courses, logical foundations of programming paradigms, verification and application research, linear common sense, higher-order good judgment, and nonmonotonic reasoning.
Read or Download Computer Science Logic: 24th International Workshop, CSL 2010, 19th Annual Conference of the EACSL, Brno, Czech Republic, August 23-27, 2010. Proceedings PDF
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Additional resources for Computer Science Logic: 24th International Workshop, CSL 2010, 19th Annual Conference of the EACSL, Brno, Czech Republic, August 23-27, 2010. Proceedings
But it is not provable in T as the witnessing algorithm would compute the inverse function to h (which is supposed to be impossible). Another example can be given by a hash function g that always outputs less bits than the input has. Then there must be a collision pair of any length: ∀x∃y1 , y2 [ y1 = y2 ∧ |x| = |y1 | = |y2 | ∧ g(y1 ) = g(y2 ) ] but this sentence cannot be provable in T as the witnessing algorithm would ﬁnd a collision pair (which is supposed to be hard). e. a polynomial time function whose range is exactly the set of propositional tautologies.
E. a string y such that S(x, y) ∧ c(x, N (x, y)) = c(x, y) . 2 NP Induction Extend T by adding as new axioms formulas expressing induction [ B(0) ∧ ∀i < x (B(i) → B(i + 1)) ] → B(x) (5) for all bounded existential formulas (the so called E1 -formulas) of the form B(x) := ∃y < s(x) C(x, y) with C an open formula. Formula C can have other free variables (parameters). Every E1 -formula deﬁnes an NP predicate and vice versa, every NP predicate can be deﬁned by such a formula. We shall call this extension of T as N P −IN D.
A proof system P has fdp if there exists a constant c ≥ 1 such that whenever a disjunction α1 ∨ . . ∨ αk (10) of k formulas with no two having a variable in common has a P -proof of size s then one of αi has a P -proof of size at most sc . A simple observation is that a proof system P that does not have fdp cannot be p-bounded. Assume for a simplicity that a P -proof of a formula is at least as long as the formula. Then all formulas αi in (10) have size at most s, at least one of them must be a tautology but it does not have p-bounded proofs.