145 research outputs found
Automata and temporal logic over arbitrary linear time
Linear temporal logic was introduced in order to reason about reactive
systems. It is often considered with respect to infinite words, to specify the
behaviour of long-running systems. One can consider more general models for
linear time, using words indexed by arbitrary linear orderings. We investigate
the connections between temporal logic and automata on linear orderings, as
introduced by Bruy\`ere and Carton. We provide a doubly exponential procedure
to compute from any LTL formula with Until, Since, and the Stavi connectives an
automaton that decides whether that formula holds on the input word. In
particular, since the emptiness problem for these automata is decidable, this
transformation gives a decision procedure for the satisfiability of the logic
Reasoning about transfinite sequences
We introduce a family of temporal logics to specify the behavior of systems
with Zeno behaviors. We extend linear-time temporal logic LTL to authorize
models admitting Zeno sequences of actions and quantitative temporal operators
indexed by ordinals replace the standard next-time and until future-time
operators. Our aim is to control such systems by designing controllers that
safely work on -sequences but interact synchronously with the system in
order to restrict their behaviors. We show that the satisfiability problem for
the logics working on -sequences is EXPSPACE-complete when the
integers are represented in binary, and PSPACE-complete with a unary
representation. To do so, we substantially extend standard results about LTL by
introducing a new class of succinct ordinal automata that can encode the
interaction between the different quantitative temporal operators.Comment: 38 page
Some Remarks on Regular Words
In the late 1970's, Courcelle introduced the class of ``arrangements'', or labeled linear ordered sets, here called just ``words''. He singled out those words which are solutions of finite systems of fixed point equations involving finite words, which we call the ``regular words''. The current paper contains some new descriptions of this class of words related to properties of regular sets of binary strings, and uses finite automata to decide various natural questions concerning these words. In particular we show that a countable word is regular iff it can be defined on an ordinary regular language (which can be chosen to be a prefix code) ordered by the lexicographical order such that the labeling function satisfies a regularity condition. Those regular words whose underlying order is ``discrete'' or ``scattered'' are characterized in several ways
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
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