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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20 Aug 2002
TL;DR: It is shown that the reachable question for some two dimensional hybrid systems are undecidable and that for other 2-dim systems this question remains unanswered, showing that it is as hard as the reachability problem for Piecewise Affine Maps, that is a well known open problem.
Abstract: We revisited decidability of the reachability problem for low dimensional hybrid systems. Even though many attempts have been done to draw the boundary between decidable and undecidable hybrid systems there are still many open problems in between. In this paper we show that the reachability question for some two dimensional hybrid systems are undecidable and that for other 2-dim systems this question remains unanswered, showing that it is as hard as the reachability problem for Piecewise Affine Maps, that is a well known open problem.
37 citations
TL;DR: The definition of a unification problem has to be modified and that the definitions of the unification types have to be adapted accordingly, and some undecidability results for the membership problem of equational theories to these classes (the 'class problem'): simplicity, almost collapse freeness, and @W-freeness are undecidable properties.
37 citations
TL;DR: It is shown that matching and unification in collapse free cquational theories behave similar with respect to the existence and the cardinality of minimal complete sets of solutions and that unification may become undecidable, if the authors add new free constants to the signature.
37 citations
TL;DR: In this paper, it was shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete.
Abstract: It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures that do not include the induced successor relation. As a special case, the EXPSPACE upper bound applies to two-variable logic over structures with two linear orders. A further consequence is that satisfiability of two-variable logic over data words with a linear order on positions and a linear order and successor relation on the data is decidable in EXPSPACE. As a complementing result, it is shown that over structures with two total preorder relations as well as over structures with one total preorder and two linear order relations, the finite satisfiability problem for two-variable logic is undecidable.
37 citations
TL;DR: In this article, a general framework is introduced to prove undecidability of fragments of theories arising in algebra and recursion theory, such as the V3V-theories of finite distributive lattices and the p.o.
Abstract: We introduce a general framework to prove undecidability of fragments. This is applied to fragments of theories arising in algebra and recursion theory. For instance, the V3V-theories of the class of finite distributive lattices and of the p.o. of recursively enumerable many-one degrees are shown to be undecidable.
37 citations