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Expressiveness of communication in answer set programming

Published online by Cambridge University Press:  01 November 2011

KIM BAUTERS
Affiliation:
Department of Applied Mathematics and Computer Science, Krijgslaan 281 (WE02), Universiteit Gent, 9000 Gent, Belgium (e-mail: kim.bauters@ugent.be, steven.schockaert@ugent.be)
STEVEN SCHOCKAERT
Affiliation:
Department of Applied Mathematics and Computer Science, Krijgslaan 281 (WE02), Universiteit Gent, 9000 Gent, Belgium (e-mail: kim.bauters@ugent.be, steven.schockaert@ugent.be)
JEROEN JANSSEN
Affiliation:
Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium (e-mail: jeroen.janssen@vub.ac.be, dirk.vermeir@vub.ac.be)
DIRK VERMEIR
Affiliation:
Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium (e-mail: jeroen.janssen@vub.ac.be, dirk.vermeir@vub.ac.be)
MARTINE DE COCK
Affiliation:
Department of Applied Mathematics and Computer Science, Krijgslaan 281 (WE02), Universiteit Gent, 9000 Gent, Belgium (e-mail: martine.decock@ugent.be)

Abstract

Answer set programming (ASP) is a form of declarative programming that allows to succinctly formulate and efficiently solve complex problems. An intuitive extension of this formalism is communicating ASP, in which multiple ASP programs collaborate to solve the problem at hand. However, the expressiveness of communicating ASP has not been thoroughly studied. In this paper, we present a systematic study of the additional expressiveness offered by allowing ASP programs to communicate. First, we consider a simple form of communication where programs are only allowed to ask questions to each other. For the most part, we deliberately consider only simple programs, i.e. programs for which computing the answer sets is in P. We find that the problem of deciding whether a literal is in some answer set of a communicating ASP program using simple communication is NP-hard. In other words, due to the ability of these simple ASP programs to communicate and collaborate, we move up a step in the polynomial hierarchy. Second, we modify the communication mechanism to also allow us to focus on a sequence of communicating programs, where each program in the sequence may successively remove some of the remaining models. This mimics a network of leaders, where the first leader has the first say and may remove models that he or she finds unsatisfactory. Using this particular communication mechanism allows us to capture the entire polynomial hierarchy. This means, in particular, that communicating ASP could be used to solve problems that are above the second level of polynomial hierarchy, such as some forms of abductive reasoning as well as PSPACE-complete problems such as STRIPS planning.

Type
Regular Papers
Copyright
Copyright © Cambridge University Press 2011

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