TY - GEN

T1 - Why so many temporal logics climb up the trees

AU - Rabinovich, Alexander

AU - Maoz, Shahar

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

PY - 2000

Y1 - 2000

N2 - Many temporal logics were suggested as branching time specification formalisms during the last 20 years. These logics were compared against each other for their expressive power, model checking complexity and succinctness. Yet, unlike the case for linear time logics, no canonical temporal logic of branching time was agreed upon. We offer an explanation for the multiplicity of temporal logics over branching time and provide an objective quantified ‘yardstick’ to measure these logics. We define an infinite hierarchy BTLk of temporal logics and prove its strictness. We show that CTL* has no finite base, and that almost all of its many sub-logics suggested in the literature are inside the second level of our hierarchy. We show that for every logic based on a finite set of modalities, the complexity of model checking is linear both in the size of structure and the size of formula.

AB - Many temporal logics were suggested as branching time specification formalisms during the last 20 years. These logics were compared against each other for their expressive power, model checking complexity and succinctness. Yet, unlike the case for linear time logics, no canonical temporal logic of branching time was agreed upon. We offer an explanation for the multiplicity of temporal logics over branching time and provide an objective quantified ‘yardstick’ to measure these logics. We define an infinite hierarchy BTLk of temporal logics and prove its strictness. We show that CTL* has no finite base, and that almost all of its many sub-logics suggested in the literature are inside the second level of our hierarchy. We show that for every logic based on a finite set of modalities, the complexity of model checking is linear both in the size of structure and the size of formula.

UR - http://www.scopus.com/inward/record.url?scp=0013360768&partnerID=8YFLogxK

U2 - 10.1007/3-540-44612-5_58

DO - 10.1007/3-540-44612-5_58

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AN - SCOPUS:0013360768

SN - 3540679014

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 629

EP - 639

BT - Mathematical Foundations of Computer Science 2000 - 25th International Symposium, MFCS 2000 , Proceedings

A2 - Rovan, Branislav

A2 - Nielsen, Mogens

PB - Springer Verlag

T2 - 25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000

Y2 - 28 August 2000 through 1 September 2000

ER -