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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Papers
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TL;DR: It is shown that system NEL is undecidable by encoding two counter machines into NEL by virtue of the faithfulness of the encoding.
28 citations
TL;DR: In this paper, it is shown that the boundedness problem is decidable for the class of FIFO networks consisting of two such CFSM's, where one of the two machines is allowed to send only a single type of message to the other.
28 citations
09 Sep 1985
TL;DR: This work constructs a special class of finite state tree transducers that are code in recognizable tree languages and proves decidability of confluence for ground term rewriting systems.
Abstract: It is well known that confluence (which is equivalent to Church-Rosser property) is undecidable for arbitrary term rewriting systems. We prove here decidability of confluence for ground term rewriting systems. To obtain this result, we construct a special class of finite state tree transducers that we code in recognizable tree languages. Our work illustrates how tree language theory is useful in term rewriting systems study and we give easily some other results in the ground case (as decidability of uniform termination).
28 citations
Posted Content•
TL;DR: In this article, it was shown that satisfiability for SPARQL patterns is undecidable in general, since the expressive power of the relational algebra is comparable with that of the SQL algebra.
Abstract: The satisfiability problem for SPARQL patterns is undecidable in general, since the expressive power of SPARQL 1.0 is comparable with that of the relational algebra. The goal of this paper is to delineate the boundary of decidability of satisfiability in terms of the constraints allowed in filter conditions. The classes of constraints considered are bound-constraints, negated bound-constraints, equalities, nonequalities, constant-equalities, and constant-nonequalities. The main result of the paper can be summarized by saying that, as soon as inconsistent filter conditions can be formed, satisfiability is undecidable. The key insight in each case is to find a way to emulate the set difference operation. Undecidability can then be obtained from a known undecidability result for the algebra of binary relations with union, composition, and set difference. When no inconsistent filter conditions can be formed, satisfiability is efficiently decidable by simple checks on bound variables and on the use of literals. The paper also points out that satisfiability for the so-called `well-designed' patterns can be decided by a check on bound variables and a check for inconsistent filter conditions.
28 citations
TL;DR: It is shown that when there are multiple agents in the language, the satisfiability problem is undecidable for APAL, GAL, and CAL, and in the single agent case, the satisfaction problem is decidable for all three logics.
Abstract: This paper demonstrates the undecidability of a number of logics with quantification over public announcements: arbitrary public announcement logic (APAL), group announcement logic (GAL), and coalition announcement logic (CAL). In APAL we consider the informative consequences of any announcement, in GAL we consider the informative consequences of a group of agents (this group may be a proper subset of the set of all agents) all of which are simultaneously (and publicly) making known announcements. So this is more restrictive than APAL. Finally, CAL is as GAL except that we now quantify over anything the agents not in that group may announce simultaneously as well. The logic CAL therefore has some features of game logic and of ATL. We show that when there are multiple agents in the language, the satisfiability problem is undecidable for APAL, GAL, and CAL. In the single agent case, the satisfiability problem is decidable for all three logics.
28 citations