Topic
Undecidable problem
About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.
Papers published on a yearly basis
Papers
More filters
•
10 Jun 2012TL;DR: It is shown that undecidability may arise even if only crisp axioms are considered, and the effectiveness of this approach is demonstrated by strengthening all previously-known undecIDability results and providing new ones.
Abstract: Fuzzy description logics (DLs) have been investigated for over two decades, due to their capacity to formalize and reason with imprecise concepts. Very recently, it has been shown that for several fuzzy DLs, reasoning becomes undecidable. Although the proofs of these results differ in the details of each specific logic considered, they are all based on the same basic idea.
In this paper, we formalize this idea and provide sufficient conditions for proving undecidability of a fuzzy DL. We demonstrate the effectiveness of our approach by strengthening all previously-known undecidability results and providing new ones. In particular, we show that undecidability may arise even if only crisp axioms are considered.
61 citations
••
26 Jun 2000TL;DR: If dead tokens are defined as those that cannot be used for firing any transition in the future, the TAPN's can detect these kind of tokens in an effective way and coverability and boundedness are proved now to be decidable.
Abstract: Timed-arc Petri nets (TAPN's) are not Turing powerful, because, in particular, they cannot simulate a counter with zero testing. Thus, we could think that this model does not increase significantly the expressiveness of untimed Petri nets. But this is not true; in a previous paper we have shown that the differences between them are big enough to make the reachability problem undecidable. On the other hand, coverability and boundedness are proved now to be decidable. This fact is a consequence of the close interrelationship between TAPN's and transfer nets, for which similar results have been recently proved. Finally, we see that if dead tokens are defined as those that cannot be used for firing any transition in the future, we can detect these kind of tokens in an effective way.
61 citations
••
25 Mar 2006TL;DR: This work considers the model-checking problem for C programs with (1) data ranging over very large domains, (2) (recursive) procedure calls, and (3) concurrent parallel components that communicate via synchronizing actions, and tackles this undecidable problem using a CounterExample Guided Abstraction Refinement (CEGAR) scheme.
Abstract: We consider the model-checking problem for C programs with (1) data ranging over very large domains, (2) (recursive) procedure calls, and (3) concurrent parallel components that communicate via synchronizing actions. We model such programs using communicating pushdown systems, and reduce the reachability problem for this model to deciding the emptiness of the intersection of two context-free languages L1 and L2. We tackle this undecidable problem using a CounterExample Guided Abstraction Refinement (CEGAR) scheme. We implemented our technique in the model checker MAGIC and found a previously unknown bug in a version of a Windows NT Bluetooth driver.
60 citations
••
TL;DR: It is shown, under reasonable complexity theoretic assumptions, that it is an undecidable problem to tell if a counting problem expressed in the framework is polynomial time computable or if it is approximable by a randomized polynometric time algorithm.
60 citations
••
07 Jul 2008TL;DR: B bounded versions of undecidable problems about context-free languages which restrict the domain of words to some finite length are considered and fully utilizing the power of incrementat SAT solvers prove correctness and validate this approach with benchmarks.
Abstract: We consider bounded versions of undecidable problems about context-free languages which restrict the domain of words to some finite length: inclusion, intersection, universality, equivalence, and ambiguity. These are in (co)-NP and thus solvable by a reduction to the (un-)satisfiability problem for propositional logic. We present such encodings --- fully utilizing the power of incrementat SAT solvers --- prove correctness and validate this approach with benchmarks.
60 citations