1,537 research outputs found
Path Checking for MTL and TPTL over Data Words
Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are
quantitative extensions of linear temporal logic, which are prominent and
widely used in the verification of real-timed systems. It was recently shown
that the path checking problem for MTL, when evaluated over finite timed words,
is in the parallel complexity class NC. In this paper, we derive precise
complexity results for the path-checking problem for MTL and TPTL when
evaluated over infinite data words over the non-negative integers. Such words
may be seen as the behaviours of one-counter machines. For this setting, we
give a complete analysis of the complexity of the path-checking problem
depending on the number of register variables and the encoding of constraint
numbers (unary or binary). As the two main results, we prove that the
path-checking problem for MTL is P-complete, whereas the path-checking problem
for TPTL is PSPACE-complete. The results yield the precise complexity of model
checking deterministic one-counter machines against formulae of MTL and TPTL
The Rank of Tree-Automatic Linear Orderings
We generalise Delhomm\'e's result that each tree-automatic ordinal is
strictly below \omega^\omega^\omega{} by showing that any tree-automatic linear
ordering has FC-rank strictly below \omega^\omega. We further investigate a
restricted form of tree-automaticity and prove that every linear ordering which
admits a tree-automatic presentation of branching complexity at most k has
FC-rank strictly below \omega^k.Comment: 20 pages, 3 figure
On the Expressiveness of TPTL and MTL over \omega-Data Words
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are
prominent extensions of Linear Temporal Logic to specify properties about data
languages. In this paper, we consider the class of data languages of
non-monotonic data words over the natural numbers. We prove that, in this
setting, TPTL is strictly more expressive than MTL. To this end, we introduce
Ehrenfeucht-Fraisse (EF) games for MTL. Using EF games for MTL, we also prove
that the MTL definability decision problem ("Given a TPTL-formula, is the
language defined by this formula definable in MTL?") is undecidable. We also
define EF games for TPTL, and we show the effect of various syntactic
restrictions on the expressiveness of MTL and TPTL.Comment: In Proceedings AFL 2014, arXiv:1405.527
Locality and information transfer in quantum operations
We investigate the situation in which no information can be transferred from
a quantum system B to a quantum system A, even though both interact with a
common system C
28th International Symposium on Temporal Representation and Reasoning (TIME 2021)
The 28th International Symposium on Temporal Representation and Reasoning (TIME 2021) was planned to take place in Klagenfurt, Austria, but had to move to an online conference due to the insecurities and restrictions caused by the pandemic. Since its frst edition in 1994, TIME Symposium is quite unique in the panorama of the scientifc conferences as its main goal is to bring together researchers from distinct research areas involving the management and representation of temporal data as well as the reasoning about temporal aspects of information. Moreover, TIME Symposium aims to bridge theoretical and applied research, as well as to serve as an interdisciplinary forum for exchange among researchers from the areas of artifcial intelligence, database management, logic and verifcation, and beyond
Topological Complexity of Locally Finite omega-Languages
to appear in Archive for Mathematical LogicInternational audienceLocally finite omega-languages were introduced by Ressayre in [Formal Languages defined by the Underlying Structure of their Words, Journal of Symbolic Logic, 53 (4), December 1988, p. 1009-1026]. These languages are defined by local sentences and extend omega-languages accepted by Büchi automata or defined by monadic second order sentences. We investigate their topological complexity. All locally finite omega languages are analytic sets, the class LOC_omega of locally finite omega-languages meets all finite levels of the Borel hierarchy and there exist some locally finite omega-languages which are Borel sets of infinite rank or even analytic but non-Borel sets. This gives partial answers to questions of Simonnet [Automates et Théorie Descriptive, Ph. D. Thesis, Université Paris 7, March 1992] and of Duparc, Finkel, and Ressayre [Computer Science and the Fine Structure of Borel Sets, Theoretical Computer Science, Volume 257 (1-2), 2001, p.85-105]
Synchronizing generalized monotonic automata
AbstractIn an earlier paper, we have studied reset words for synchronizing automatawhose states admit a stable linear order. Here we show that the same bound on the length of the shortest reset word persists for synchronizing automatasatisfying much weaker stability restriction. This result supports our conjecture concerning the length of reset words for synchronizing automataaccepting only star-free languages
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