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(5)
Expressive Power
Logic In Computer Science
Temporal Logic
Timed Automata
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On Expressive Powers of Timed Logics: Comparing Boundedness, Nonpunctuality and Deterministic Freezing
On Expressive Powers of Timed Logics: Comparing Boundedness, Nonpunctuality and Deterministic Freezing,10.1007/9783642232176_5,Computing Research
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On Expressive Powers of Timed Logics: Comparing Boundedness, Nonpunctuality and Deterministic Freezing
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Paritosh K. Pandya
,
Simoni S. Shah
Timed temporal logics exhibit a bewildering diversity of operators and the resulting decidability and expressiveness properties also vary considerably. We study the expressive powers of timed logics TPTL[U,S] and MTL[U,S] as well as their several fragments. Extending the LTL EF games of Etessami and Wilke, we define MTL EhrenfeuchtFraisse games on a pair of timed words. Using the associated EF theorem we show that, expressively, the timed logics BoundedMTL[U,S], MTL[F,P] and MITL[U,S] (respectively incorporating the restrictions of boundedness, unary modalities and nonpunctuality), are all pairwise incomparable. Going to more expressive logics, we show that MTL[U,S] is expressively incomparable with the unary freeze logic TPTL[F,P] extending the result of Bouyer et al. Finally, we consider the deterministic freeze logic TTL[X,Y], which is expressively equivalent to partially ordered 2way deterministic
timed automata
(po2DTA). As our second main result, we show by explicit reductions that TTL[X,Y] lies strictly between the unary, nonpunctual logic MITL[F,P] and its bounded fragment BoundedMITL[F,P]. This shows that deterministic punctuality is expressible by the nonpunctual MITL[F,P].
Journal:
Computing Research Repository  CORR
, vol. abs/1102.5, 2011
DOI:
10.1007/9783642232176_5
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References
(16)
Marking the chops: an unambiguous temporal logic
(
Citations: 10
)
Kamal Lodaya
,
Paritosh K. Pandya
,
Simoni S. Shah
Conference:
IFIP International Conference on Theoretical Computer Science  IFIP TCS
, pp. 461476, 2008
Weak Alternating Timed Automata
(
Citations: 4
)
Pawel Parys
,
Igor Walukiewicz
Conference:
International Colloquium on Automata, Languages and Programming  ICALP
, pp. 273284, 2009
Realtime Logics: Complexity and Expressiveness
(
Citations: 260
)
Rajeev Alur
,
Thomas A. Henzinger
Conference:
Logic in Computer Science  LICS
, pp. 390401, 1990
Back to the Future: Towards a Theory of Timed Regular Languages
(
Citations: 50
)
Rajeev Alur
,
Thomas A. Henzinger
Conference:
IEEE Symposium on Foundations of Computer Science  FOCS
, pp. 177186, 1992
A Really Temporal Logic
(
Citations: 336
)
Rajeev Alur
,
Thomas A. Henzinger
Conference:
IEEE Symposium on Foundations of Computer Science  FOCS
, pp. 164169, 1994