Wyniki wyszukiwania - BazTech

1

Level Mapping Induced Loop Formulas forWeight Constraint and Aggregate Logic Programs

Liu G., You J-H.

Fundamenta Informaticae

|

2011

|

Vol. 106, nr 1

25-43

EN

Level mapping and loop formulas are two different means to justify and characterize answer sets for normal logic programs. Both of them specify conditions under which a supported model is an answer set. Though serving a similar purpose, in the past the two have been studied largely in isolation with each other. In this paper, we study level mapping and loop formulas for weight constraint and aggregate (logic) programs. We show that, for these classes of programs, loop formulas can be devised from level mapping characterizations. First, we formulate a level mapping characterization of stable models and show that it leads to a new formulation of loop formulas for arbitrary weight constraint programs, without using any new atoms. This extends a previous result on loop formulas for weight constraint programs, where weight constraints contain only positive literals. Second, since aggregate programs are closely related to weight constraint programs, we further use level mapping to characterize the underlying answer set semantics based on which we formulate loop formulas for aggregate programs. The main result is that for aggregate programs not involving the inequality comparison operator, the dependency graphs can be built in polynomial time. This compares to the previously known exponential time method.

2

Level Mapping Induced Loop Formulas for Weight Constraint and Aggregate Logic Programs

Liu G., You J-H.

Fundamenta Informaticae

|

2010

|

Vol. 101, nr 3

237-255

EN

Level mapping and loop formulas are two different means to justify and characterize answer sets for normal logic programs. Both of them specify conditions under which a supported model is an answer set. Though serving a similar purpose, in the past the two have been studied largely in isolation with each other. In this paper, we study level mapping and loop formulas for weight constraint and aggregate (logic) programs. We show that, for these classes of programs, loop formulas can be devised from level mapping characterizations. First, we formulate a level mapping characterization of stable models and show that it leads to a new formulation of loop formulas for arbitrary weight constraint programs, without using any new atoms. This extends a previous result on loop formulas for weight constraint programs, where weight constraints contain only positive literals. Second, since aggregate programs are closely related to weight constraint programs, we further use level mapping to characterize the underlying answer set semantics based on which we formulate loop formulas for aggregate programs. The main result is that for aggregate programs not involving the inequality comparison operator, the dependency graphs can be built in polynomial time. This compares to the previously known exponential time method.

3

Using logic programs with stable model semantics to solve deadlock and reachability problems for 1-safe Petri Nets

Heljanko K.

Fundamenta Informaticae

|

1999

|

Vol. 37, Nr 3

247-268

EN

McMillan has presented a deadlock detection method for Petri nets based on finite complete prefixes (i.e. net unfoldings). The approach transforms the PSPACE-complete deadlock detec-tion problem for a 1-safe Petri net into a potentially exponentially larger NP-complete prob-lem of deadlock detection for a finite complete prefix. McMillan devised a branch-and-bound algorithm for deadlock detection in prefixes. Recently, Melzer and Römer have presented another approach, which is based on solving mixed integer programming problems. In this work it is shown that instead of using mixed integer programming, a constraint-based logic programming framework can be employed, and a linear-size, translation from deadlock detec-tion in prefixes into the problem of finding a stable model of a logic program is presented. As a side result also such a translation for solving the reachability problem is devised. Correct-ness proofs of both the translations are presented. Experimental results are given from an im-plementation combining the prefix generator of the PEP-tool, the translation, and an imple-mentation of a constraint-based logic programming framework, the smodels system. The ex-periments show the proposed approach to be quite competitive, when compared to the ap-proaches of McMillan and Melzer/Römer.