Theoretical Computer Science
The benefits of relaxing punctuality
Journal of the ACM (JACM)
Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Automata and Computability
Partially-Ordered Two-Way Automata: A New Characterization of DA
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Logics and Models of Real Time: A Survey
Proceedings of the Real-Time: Theory in Practice, REX Workshop
First-order logic with two variables and unary temporal logic
Information and Computation - Special issue: LICS'97
Back to the future: towards a theory of timed regular languages
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
DLT'10 Proceedings of the 14th international conference on Developments in language theory
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
The unary fragments of metric interval temporal logic: bounded versus lower bound constraints
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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Unambiguous languages (UL), originally defined by Schutzenberger using unambiguous polynomials, are a robust subclass of regular languages. They have many diverse characterizations: they are recognized by partially-ordered two-way deterministic automata (po2dfa), they are definable by Unary Temporal Logic (UTL) as also by the two variable first-order logic over words (FO2[ In this paper, we consider the timed version of unambiguous languages. A subclass of the two-way deterministic timed automata (2DTA) of Alur and Henzinger, called partially-ordered two-way deterministic automata (po2DTA) are examined and we call the languages accepted by these as Timed Unambiguous Languages (TUL). This class has some interesting properties: we show that po2DTA are boolean closed and their non-emptiness is NP-Complete. We propose a deterministic and unary variant of MTL called DUMTL and show that DUMTL formulae can be reduced to language equivalent po2DTA in polynomial time, giving NP-complete satisfiability for the logic. Moreover, DUMTL is shown to be expressively complete for po2DTA. Finally, we consider the unary fragments of well known logics MTL and MITL and we show that neither of these are expressively equivalent to po2DTA. Contrast this with the untimed case where unary temporal logic is equivalent to po2dfa.