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Temporal Representation and Reasoning, International Syposium on (2005)
Burlington, Vermont
June 23, 2005 to June 25, 2005
ISSN: 1530-1311
ISBN: 0-7695-2370-6
pp: 138-146
Dirk Walther , University of Liverpool
Frank Wolter , University of Liverpool
Carsten Lutz , Technical University Dresden
Often, the addition of metric operators to qualitative temporal logics leads to an increase of the complexity of satisfiability by at least one exponential. In this paper, we exhibit a number of metric extensions of qualitative temporal logics of the real line that do not lead to an increase in computational complexity. We show that the language obtained by extending since/until logic of the real line with the operators ?sometime within n time units?, n coded in binary, is PSPACE-complete even without the finite variability assumption. Without qualitative temporal operators the complexity of this language turns out to depend on whether binary or unary coding of parameters is assumed: it is still PSPACE-hard under binary coding but in NP under unary coding.
Dirk Walther, Frank Wolter, Carsten Lutz, "Quantitative Temporal Logics: PSPACE and Below", Temporal Representation and Reasoning, International Syposium on, vol. 00, no. , pp. 138-146, 2005, doi:10.1109/TIME.2005.31
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