Abstract
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 ( FO 2[<]).
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.
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Pandya, P.K., Shah, S.S. (2010). Unambiguity in Timed Regular Languages: Automata and Logics. In: Chatterjee, K., Henzinger, T.A. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2010. Lecture Notes in Computer Science, vol 6246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15297-9_14
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DOI: https://doi.org/10.1007/978-3-642-15297-9_14
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