Unambiguity in Timed Regular Languages: Automata and Logics

  title={Unambiguity in Timed Regular Languages: Automata and Logics},
  author={Paritosh K. Pandya and Simoni S. Shah},
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… 
Deterministic Logics for UL
This paper considers three such deterministic logics with varied modalities, namely TL[X a ,Y a ],TL[Ũ,S] and UITL ±, and shows that they all characterize UL, and have NP-complete satisfiability.
On Expressive Powers of Timed Logics: Comparing Boundedness, Non-punctuality, and Deterministic Freezing
This paper defines MTL Ehrenfeucht-Fraisse games on a pair of timed words and relates the expressiveness of a recently proposed deterministic freeze logic TTL[Xθ, Yθ] to MTL, and shows that deterministic freezing with punctuality is expressible in the non-punctual MITL[FI, PI].
Automated Technology for Verification and Analysis
It is shown that MITL[F∞,P∞] which has unary modalities with only lower-bound constraints is (surprisingly) expressively complete for Partially Ordered 2-Way Deterministic Timed Automata (po2DTA) and the reduction from logic to automaton gives us its NP-complete satisfiability.
Dynamic contracts for verification and enforcement of real-time systems properties
Programa de Doutoramento em Informatica (MAP-i) das Universidades do Minho, de Aveiro e do Porto está disponible nos seminários preliminarias de 2017-18.
The Unary Fragments of Metric Interval Temporal Logic: Bounded versus Lower Bound Constraints
A comprehensive picture of the decidability and expressiveness of various unary fragments of MITL is provided, which shows that the fragment having unary modalities with only bounded intervals has NEXPTIME-complete satisfiability.


Back to the future: towards a theory of timed regular languages
  • R. Alur, T. Henzinger
  • Computer Science
    Proceedings., 33rd Annual Symposium on Foundations of Computer Science
  • 1992
The authors show that the resulting class of bounded two-way deterministic timed automata is closed under all boolean operations, has decidable (PSPACE-complete) emptiness and inclusion problems, and subsumes all decidable real-time logics the authors know.
A Theory of Timed Automata
Marking the chops: an unambiguous temporal logic
This paper defines a sublogic of Interval Temporal Logic by replacing chops with marked chops but without any restriction on the alternation depth, and shows that the resulting logic admits unique parsing of a word matching a formula.
Partially-Ordered Two-Way Automata: A New Characterization of DA
It is proved that partially-ordered 2-way DFAs recognize exactly the class UL of unambiguous languages introduced by Schutzenberger in 1976 and exactly those languages whose syntactic monoid is in DA.
Around Dot Depth Two
This paper extends the earlier work [LPS08] to propose partially-ordered two-way deterministic finite automata with look-around (po2dla) and a new interval temporal logic called LITL and shows that they also characterize the variety DA*D.
On the decidability and complexity of Metric Temporal Logic over finite words
It is shown that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity, and model checking the safety fragment of MTL--which includes invariance and time-bounded response properties--is also decidable.
Over words, two variables are as powerful as one quantifier alternation
It is shown that the problem of determining whether or not a given temporal string property belongs to UTL is decidable (in exponential space), which settles a hitherto open problem.
Logics and Models of Real Time: A Survey
We survey logic-based and automata-based languages and techniques for the specification and verification of real-time systems. In particular, we discuss three syntactic extensions of temporal logic:
First-order logic with two variables and unary temporal logic
It is proved that FO/sup 2/ can express precisely the same properties as linear temporal logic with only the unary temporal operators: "next", "previously", "sometime in the future", and "s sometime in the past", a logic the authors denote by unary-TL.
Real-Time: Theory in Practice: Rex Workshop, Mook, the Netherlands, June 3-7, 1991: Proceedings
An old-fashioned recipe for real time verifying automata specifications of probabilistic real-time systems and a specification of the cat and mouse problem.