Quantitative Temporal Logics: PSPACE and Below

C. Lutz, D. Walther, F. Wolter
12th International Symposium on Temporal Representation and Reasoning (TIME'05)  
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
more » ... ithout 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.
doi:10.1109/time.2005.31 dblp:conf/time/LutzWW05 fatcat:yey2vpohqzfnthf55bmdbgteue