The Ultimate Undecidability Result for the Halpern-Shoham Logic

2011 ◽  
Author(s):  
Jerzy Marcinkowski ◽  
Jakub Michaliszyn
Keyword(s):  
Undecidability Result

RESTRICTED SETS OF TRAJECTORIES AND DECIDABILITY OF SHUFFLE DECOMPOSITIONS

2005 ◽  
Vol 16 (05) ◽  
pp. 897-912 ◽  
Author(s):  
MICHAEL DOMARATZKI ◽  
KAI SALOMAA
Keyword(s):  
Regular Languages ◽  
Decomposition Problem ◽  
Open Question ◽  
Free Set ◽  
Context Free ◽  
Undecidability Result

The decidability of the shuffle decomposition problem for regular languages is a long standing open question. We consider decompositions of regular languages with respect to shuffle along a regular set of trajectories and obtain positive decidability results for restricted classes of trajectories. Also we consider decompositions of unary regular languages. Finally, we establish in the spirit of the Dassow-Hinz undecidability result an undecidability result for regular languages shuffled along a fixed linear context-free set of trajectories.

Two variable first-order logic over ordered domains

2001 ◽  
Vol 66 (2) ◽  
pp. 685-702 ◽  
Author(s):  
Martin Otto
Keyword(s):  
Order Logic ◽  
Decision Problems ◽  
First Order Logic ◽  
Satisfiability Problem ◽  
Exponential Time ◽  
Infinite Domains ◽  
First Order ◽  
Computation Tree ◽  
Common Extension ◽  
Undecidability Result

AbstractThe satisfiability problem for the two-variable fragment of first-order logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations.It is shown that FO2 over ordered, respectively wellordered. domains or in the presence of one well-founded relation, is decidable for satisfiability as well as for finite satisfiability. Actually the complexity of these decision problems is essentially the same as for plain unconstrained FO2. namely non-deterministic exponential time.In contrast FO2 becomes undecidable for satisfiability and for finite satisfiability, if a sufficiently large number of predicates are required to be interpreted as orderings. wellorderings. or as arbitrary wellfounded relations. This undecidability result also entails the undecidability of the natural common extension of FO2 and computation tree logic CTL.

Effectively extensible theories

1968 ◽  
Vol 33 (1) ◽  
pp. 56-68 ◽  
Author(s):  
Marian Boykan Pour-El
Keyword(s):  
Number Theory ◽  
Strong Form ◽  
Specific Formulation ◽  
Undecidability Result

It is well known that Gödel's famous undecidability result may be viewed in the following strong form. Suppose we are given a specific presentation (i.e., a specific formulation in terms of axioms and rules of inference) of number theory. Then there exists an effective method which, when applied to a consistent axiomatizable extension of the theory yields an undecidable sentence of this extension. For distinct presentations the undecidable sentences obtained would be distinct. This is because the sentence constructed depends upon the notion of proof and hence ultimately upon the axioms and rules of inference—i.e., upon the specific presentation.

scholarly journals On the Expressive Power of Concurrent Constraint Programming Languages

2002 ◽  
Vol 9 (22) ◽  
Author(s):  
Mogens Nielsen ◽  
Catuscia Palamidessi ◽  
Frank D. Valencia
Keyword(s):  
Programming Languages ◽  
Constraint Programming ◽  
Expressive Power ◽  
Finite Domain ◽  
Process Variables ◽  
Recursive Procedures ◽  
Undecidability Result ◽  
Concurrent Constraint Programming

The tcc paradigm is a formalism for timed concurrent constraint programming. Several tcc languages differing in their way of expressing infinite behaviour have been proposed in the literature. In this paper we study the expressive power of some of these languages. In particular, we show that:<dl compact="compact"><dt>(1)</dt><dd>recursive procedures with parameters can be encoded into parameterless recursive procedures with dynamic scoping, and vice-versa.</dd><dt>(2)</dt><dd>replication can be encoded into parameterless recursive procedures with static scoping, and vice-versa.</dd><dt>(3)</dt><dd>the languages from (1) are strictly more expressive than the languages from (2).</dd></dl>Furthermore, we show that behavioural equivalence is undecidable for the languages from (1), but decidable for the languages from (2). The undecidability result holds even if the process variables take values from a fixed finite domain.

scholarly journals On the Satisfiability Problem for SPARQL Patterns

2016 ◽  
Vol 56 ◽  
pp. 403-428 ◽  
Author(s):  
Xiaowang Zhang ◽  
Jan Van den Bussche ◽  
François Picalausa
Keyword(s):  
Relational Algebra ◽  
Satisfiability Problem ◽  
Binary Relations ◽  
Bound Constraints ◽  
Np Complete ◽  
Difference Operation ◽  
Undecidability Result

The satisfiability problem for SPARQL 1.0 patterns is undecidable in general, since the relational algebra can be emulated using such patterns. 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 decidable by syntactic checks on bound variables and on the use of literals. Although the problem is shown to be NP-complete, it is experimentally shown that the checks can be implemented efficiently in practice. 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.

scholarly journals A family of groups with nice word problems

1974 ◽  
Vol 17 (4) ◽  
pp. 414-425 ◽  
Author(s):  
Verena Huber Dyson
Keyword(s):  
Word Problem ◽  
Finite Groups ◽  
Word Problems ◽  
Elementary Theory ◽  
Negative Solution ◽  
Open Sentence ◽  
Undecidability Result

This paper is an outgrowth of my old battle with the open sentence problem for the theory of finite groups. The unsolvability of the word problem for groups (cf. [1] and [4]) entails the undecidability of the open sentence problem for the elementary theory of groups and thus strengthens the original undecidability result for this theory (cf. [7]). The fact that the elementary theory of finite groups is also undecidable (cf. [2] and [6]) therefore justifies my interest in the open sentence problem for that theory. This paper contains a construction of groups that might lead to a negative solution.

scholarly journals An undecidability result for AGh

2006 ◽  
Vol 368 (1-2) ◽  
pp. 161-167 ◽  
Author(s):  
Stéphanie Delaune
Keyword(s):  
Undecidability Result

scholarly journals An Undecidability Result on Limits of Sparse Graphs

10.37236/2340 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Endre Csóka
Keyword(s):  
Random Graph ◽  
Bounded Degree ◽  
Sparse Graphs ◽  
Random Node ◽  
Bounded Degree Graphs ◽  
Undecidability Result

Given a set $\mathcal{B}$ of finite rooted graphs and a radius $r$ as an input, we prove that it is undecidable to determine whether there exists a sequence $(G_i)$ of finite bounded degree graphs such that the rooted $r$-radius neighbourhood of a random node of $G_i$ is isomorphic to a rooted graph in $\mathcal{B}$ with probability tending to 1. Our proof implies a similar result for the case where the sequence $(G_i)$ is replaced by a unimodular random graph.

scholarly journals Hereditary History Preserving Bisimilarity is Undecidable

1999 ◽  
Vol 6 (19) ◽  
Author(s):  
Marcin Jurdzinski ◽  
Mogens Nielsen
Keyword(s):  
Petri Nets ◽  
Transition Systems ◽  
Halting Problem ◽  
Proper Subclass ◽  
Intermediate Problem ◽  
Tiling Systems ◽  
Counter Machines ◽  
Undecidability Result

We show undecidability of hereditary history preserving bisimilarity<br />for finite asynchronous transition systems by a reduction from the halting<br />problem of deterministic 2-counter machines. To make the proof more<br />transparent we introduce an intermediate problem of checking domino<br />bisimilarity for origin constrained tiling systems. First we reduce the<br />halting problem of deterministic 2-counter machines to origin constrained<br />domino bisimilarity. Then we show how to model domino bisimulations as<br />hereditary history preserving bisimulations for finite asynchronous transitions<br />systems. We also argue that the undecidability result holds for<br />finite 1-safe Petri nets, which can be seen as a proper subclass of finite<br />asynchronous transition systems.

scholarly journals Sticky Existential Rules and Disjunction are Incompatible

2021 ◽  
Author(s):  
Michael Morak
Keyword(s):  
Query Answering ◽  
Fixed Set ◽  
Existential Quantification ◽  
Undecidability Result

Stickiness is one of the well-known properties in the literature that guarantees decidability of query answering under sets of existential rules, that is, Datalog rules extended with existential quantification in rule heads. In this note, we investigate whether this remains true in the case when rule heads are allowed to be disjunctive. We answer this question in the negative, providing a strong undecidability result that shows that the concept of stickiness cannot be extended to disjunctive existential rules, even when considering only fixed atomic queries and a fixed set of rules. This provides evidence that, in order to keep query answering decidable, a stronger property than stickiness is needed in the disjunctive case.

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