Topic
Undecidable problem
About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.
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TL;DR: This article establishes that this is the case for very simple languages, namely for safety and reachability specifications in the intersection of LTL and ACTL, that distributed synthesis in the classical setting is undecidable for very weak languages.
22 citations
TL;DR: In this paper, it was shown that the problem of embeddability of finite semigroup amalgamations is undecidable and that the embedding problem for finite 4-nil-potent semigroups is also undecidability.
22 citations
03 Jun 2004
TL;DR: In this article, an abstraction for the safety property of a transition system given by a term rewriting system is given, which is automatically generated from a given TRS by using abstract interpretation, and there are some cases in which the problem can be decided.
Abstract: Verifying the safety property of a transition system given by a term rewriting system is an undecidable problem. In this paper, we give an abstraction for the problem which is automatically generated from a given TRS by using abstract interpretation. Then we show that there are some cases in which the problem can be decided. Also we show a new decidable subclass of term rewriting systems which effectively preserves recognizability.
22 citations
Journal Article•
TL;DR: It is shown that the problem is decidable for wPRS if the problem remains undecidable for PA processes even with respect to the LTL fragment with the only modality until or the fragment with modalities next and infinitely often.
Abstract: We establish a decidability boundary of the model checking problem for infinite-state systems defined by Process Rewrite Systems (PRS) or weakly extended Process Rewrite Systems (wPRS), and properties described by basic fragments of action-based Linear Temporal Logic (LTL). It is known that the problem for general LTL properties is decidable for Petri nets and for pushdown processes, while it is undecidable for PA processes. As our main result, we show that the problem is decidable for wPRS if we consider properties defined by formulae with only modalities strict eventually and strict always. Moreover, we show that the problem remains undecidable for PA processes even with respect to the LTL fragment with the only modality until or the fragment with modalities next and infinitely often.
22 citations
20 Sep 2006
TL;DR: It is proved that the properties of reachability, joinability and confluence are undecidable for flat TRSs.
Abstract: We prove that the properties of reachability, joinability and confluence are undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one.
22 citations