44,707 research outputs found
On optimal heuristic randomized semidecision procedures, with application to proof complexity
The existence of a (p-)optimal propositional proof system is a major open
question in (proof) complexity; many people conjecture that such systems do not
exist. Krajicek and Pudlak (1989) show that this question is equivalent to the
existence of an algorithm that is optimal on all propositional tautologies.
Monroe (2009) recently gave a conjecture implying that such algorithm does not
exist.
We show that in the presence of errors such optimal algorithms do exist. The
concept is motivated by the notion of heuristic algorithms. Namely, we allow
the algorithm to claim a small number of false "theorems" (according to any
samplable distribution on non-tautologies) and err with bounded probability on
other inputs.
Our result can also be viewed as the existence of an optimal proof system in
a class of proof systems obtained by generalizing automatizable proof systems.Comment: 11 pages, accepted to STACS 201
Practical Reasoning for Very Expressive Description Logics
Description Logics (DLs) are a family of knowledge representation formalisms
mainly characterised by constructors to build complex concepts and roles from
atomic ones. Expressive role constructors are important in many applications,
but can be computationally problematical. We present an algorithm that decides
satisfiability of the DL ALC extended with transitive and inverse roles and
functional restrictions with respect to general concept inclusion axioms and
role hierarchies; early experiments indicate that this algorithm is well-suited
for implementation. Additionally, we show that ALC extended with just
transitive and inverse roles is still in PSPACE. We investigate the limits of
decidability for this family of DLs, showing that relaxing the constraints
placed on the kinds of roles used in number restrictions leads to the
undecidability of all inference problems. Finally, we describe a number of
optimisation techniques that are crucial in obtaining implementations of the
decision procedures, which, despite the worst-case complexity of the problem,
exhibit good performance with real-life problems
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