542 research outputs found
A feasible interpolation for random resolution
Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is
a sound propositional proof system that extends the resolution proof system by
the possibility to augment any set of initial clauses by a set of randomly
chosen clauses (modulo a technical condition). We show how to apply the general
feasible interpolation theorem for semantic derivations of Krajicek (JSL, 1997)
to random resolution. As a consequence we get a lower bound for random
resolution refutations of the clique-coloring formulas.Comment: Preprint April 2016, revised September and October 201
Automating Resolution is NP-Hard
We show that the problem of finding a Resolution refutation that is at most
polynomially longer than a shortest one is NP-hard. In the parlance of proof
complexity, Resolution is not automatizable unless P = NP. Indeed, we show it
is NP-hard to distinguish between formulas that have Resolution refutations of
polynomial length and those that do not have subexponential length refutations.
This also implies that Resolution is not automatizable in subexponential time
or quasi-polynomial time unless NP is included in SUBEXP or QP, respectively
Mathematical Logic: Proof Theory, Constructive Mathematics
[no abstract available
A Complexity Gap for Tree-Resolution
It is shown that any sequence psi_n of tautologies which expresses thevalidity of a fixed combinatorial principle either is "easy" i.e. has polynomialsize tree-resolution proofs or is "difficult" i.e requires exponentialsize tree-resolution proofs. It is shown that the class of tautologies whichare hard (for tree-resolution) is identical to the class of tautologies whichare based on combinatorial principles which are violated for infinite sets.Actually it is shown that the gap-phenomena is valid for tautologies basedon infinite mathematical theories (i.e. not just based on a single proposition).We clarify the link between translating combinatorial principles (ormore general statements from predicate logic) and the recent idea of using the symmetrical group to generate problems of propositional logic.Finally, we show that it is undecidable whether a sequence psi_n (of thekind we consider) has polynomial size tree-resolution proofs or requiresexponential size tree-resolution proofs. Also we show that the degree ofthe polynomial in the polynomial size (in case it exists) is non-recursive,but semi-decidable.Keywords: Logical aspects of Complexity, Propositional proof complexity,Resolution proofs.
Interpolant-Based Transition Relation Approximation
In predicate abstraction, exact image computation is problematic, requiring
in the worst case an exponential number of calls to a decision procedure. For
this reason, software model checkers typically use a weak approximation of the
image. This can result in a failure to prove a property, even given an adequate
set of predicates. We present an interpolant-based method for strengthening the
abstract transition relation in case of such failures. This approach guarantees
convergence given an adequate set of predicates, without requiring an exact
image computation. We show empirically that the method converges more rapidly
than an earlier method based on counterexample analysis.Comment: Conference Version at CAV 2005. 17 Pages, 9 Figure
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