scholarly journals Relating timed and register automata

2014 ◽  
Vol 26 (6) ◽  
pp. 993-1021 ◽  
Author(s):  
DIEGO FIGUEIRA ◽  
PIOTR HOFMAN ◽  
SŁAWOMIR LASOTA
Keyword(s):  
Decision Problems ◽  
Models Of Computation ◽  
Exponential Time ◽  
Infinite Words ◽  
Complexity Results ◽  
Ordered Data ◽  
Decidability And Complexity ◽  
Alternating Automata ◽  
Primitive Recursive ◽  
Timed Automaton

Timed and register automata are well-known models of computation over timed and data words, respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two models behave differently in appearance, several decision problems have the same (un)decidability and complexity results for both models. As a prominent example, emptiness is decidable for alternating automata with one clock or register, both with non-primitive recursive complexity. This is not by chance.This work confirms that there is indeed a tight relationship between the two models. We show that a run of a timed automaton can be simulated by a register automaton over ordered data domain, and conversely that a run of a register automaton can be simulated by a timed automaton. These are exponential time reductions hold both in the finite and infinite words settings. Our results allow to transfer decidability results back and forth between these two kinds of models, as well complexity results modulo an exponential time reduction. We justify the usefulness of these reductions by obtaining new results on register automata.

scholarly journals Mīmāṃsā deontic reasoning using specificity: a proof theoretic approach

2020 ◽  
Author(s):  
Björn Lellmann ◽  
Francesca Gulisano ◽  
Agata Ciabattoni
Keyword(s):  
Deontic Logic ◽  
Sequent Calculus ◽  
Prima Facie ◽  
Theoretic Approach ◽  
Deontic Reasoning ◽  
Complexity Results ◽  
Restricted Form ◽  
Philosophical School ◽  
Decidability And Complexity ◽  
Potential Use

Abstract Over the course of more than two millennia the philosophical school of Mīmāṃsā has thoroughly analyzed normative statements. In this paper we approach a formalization of the deontic system which is applied but never explicitly discussed in Mīmāṃsā to resolve conflicts between deontic statements by giving preference to the more specific ones. We first extend with prohibitions and recommendations the non-normal deontic logic extracted in Ciabattoni et al. (in: TABLEAUX 2015, volume 9323 of LNCS, Springer, 2015) from Mīmāṃsā texts, obtaining a multimodal dyadic version of the deontic logic $$\mathsf {MD}$$ MD . Sequent calculus is then used to close a set of prima-facie injunctions under a restricted form of monotonicity, using specificity to avoid conflicts. We establish decidability and complexity results, and investigate the potential use of the resulting system for Mīmāṃsā philosophy and, more generally, for the formal interpretation of normative statements.

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.

The complexity of weakly recognizing morphisms

2018 ◽  
Vol 53 (1-2) ◽  
pp. 1-17
Author(s):  
Lukas Fleischer ◽  
Manfred Kufleitner
Keyword(s):  
Computational Complexity ◽  
Regular Languages ◽  
Decision Problems ◽  
Membership Problem ◽  
Surjective Morphism ◽  
Infinite Words ◽  
Descriptional Complexity ◽  
Emptiness Problem ◽  
Free Semigroups ◽  
Büchi Automaton

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We study the descriptional complexity of various constructions and the computational complexity of various decision problems for weakly recognizing morphisms. The constructions we consider are the conversion from and to Büchi automata, the conversion into strongly recognizing morphisms, as well as complementation. We also show that the fixed membership problem is NC1-complete, the general membership problem is in L and that the inclusion, equivalence and universality problems are NL-complete. The emptiness problem is shown to be NL-complete if the input is given as a non-surjective morphism.

scholarly journals On Confluent Semi-commutations: Decidability and Complexity Results

1994 ◽  
Vol 110 (1) ◽  
pp. 164-182 ◽  
Author(s):  
V. Diekert ◽  
E. Ochmanski ◽  
K. Reinhardt
Keyword(s):  
Complexity Results ◽  
Decidability And Complexity

scholarly journals Query Answering with Transitive and Linear-Ordered Data

2018 ◽  
Vol 63 ◽  
pp. 191-264
Author(s):  
Antone Amarilli ◽  
Michael Benedikt ◽  
Pierre Bourhis ◽  
Michael Vanden Boom
Keyword(s):  
Linear Order ◽  
Transitive Closure ◽  
Query Answering ◽  
Decision Problems ◽  
Natural Variants ◽  
Powerful Constraint ◽  
Ordered Data ◽  
Constraint Languages

We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation to be transitive, restricting a relation to be the transitive closure of another relation, and restricting a relation to be a linear order. We give some natural variants of guardedness that allow inference to be decidable in each case, and isolate the complexity of the corresponding decision problems. Finally we show that slight changes in these conditions lead to undecidability.

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