On O-Minimal Hybrid Systems

Brihaye, Thomas; Michaux, Christian; Rivière, Cédric; Troestler, Christophe

doi:10.1007/978-3-540-24743-2_15

Cited by 36 publications

(74 citation statements)

References 14 publications

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“…An interesting class of hybrid automata is the class of o-minimal automata [5,6]. The formulae Dyn(v), Inv(v), Act(e), and Res(e) of such automata are defined in a o-minimal theory for each v ∈ V and e ∈ E. Moreover, their resets are constant, i.e., they do not depend on the point from which the edge is crossed.…”

Section: Basic Notionsmentioning

confidence: 99%

Decidable Compositions of O-Minimal Automata

Casagrande

Corvaja

Piazza

et al. 2008

Automated Technology for Verification and Analysis

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Abstract. We identify a new class of decidable hybrid automata: namely, parallel compositions of semi-algebraic o-minimal automata. The class we consider is fundamental to hierarchical modeling in many exemplar systems, both natural and engineered. Unfortunately, parallel composition, which is an atomic operator in such constructions, does not preserve the decidability of reachability. Luckily, this paper is able to show that when one focuses on the composition of semi-algebraic o-minimal automata, it is possible to translate the decidability problem into a satisfiability problem over formulae involving both real and integer variables. While in the general case such formulae would be undecidable, the particular format of the formulae obtained in our translation allows combining decidability results stemming from both algebraic number theory and first-order logic over (R, 0, 1, +, * , <) to yield a novel decidability algorithm. From a more general perspective, this paper exposes many new open questions about decidable combinations of real/integer logics.

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Section: Basic Notionsmentioning

confidence: 99%

Decidable Compositions of O-Minimal Automata

Casagrande

Corvaja

Piazza

et al. 2008

Automated Technology for Verification and Analysis

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“…We conclude this section citing the works in [15,6] where the issue of extending o-minimal automata relaxing the constant reset constraint is taken into consideration, and some extensions leading to undecidability are presented.…”

Section: Is It Possible To Decide If a Region Is Reachable Within A Tmentioning

confidence: 99%

“…Hence, by using, for example, Collins cylindric algebraic decomposition algorithm [6] we can eliminate the quantifiers in ψ (l j i ,l i p ) (t 0 ) and obtain a real algebraic number witnessing (the unique) timevalue satisfying ψ (l j i ,l i p ) (t 0 ). We use the computed greatest lower bound, say α, to label the edge (l j i , l i p ) in G. We also distinguish the case in which α is the left extreme of an open interval of times, from the case in which α is the left extreme of a closed interval of times (allowing to pass from R(l j , l i ) to …”

Section: Are the Following Of(r) First-order Formulasmentioning

confidence: 99%

Reachability Problems on Extended O-Minimal Hybrid Automata

Gentilini

2005

Lecture Notes in Computer Science

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Abstract. Within hybrid systems theory, o-minimal automata are often considered on the border between decidability and undecidability. In such classes of hybrid automata, the constraint of having only constant reset upon discrete jumps is a strong limitation for their applicability: hence, an important issue for both theoreticians and practitioners, is that of relaxing the above constraint, while not fall into undecidability.In this paper we start considering the problem of timed-bounded reachability on o-minimal automata. This can be seen either as a reachability problem paired with time-constraints or as a classical reachability problem for a class of hybrid automata which properly extends the o-minimal one, with an extra variable representing time. Then, we directly face the problem of extending o-minimal automata by allowing some variables to retain their values upon a discrete jump, without crossing the undecidability border.

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“…A timed transition followed by a discrete one will be called a timed action. Allowing an arbitrary number of continuous transitions prior to a discrete one, without the requirement of o-minimality, renders it impossible to construct a bisimulation of finite index [15,16].…”

Section: Introductionmentioning

confidence: 99%

Average-price-per-reward games on hybrid automata with strong resets

Rutkowski

Lazić

Jurdziński

2010

Int J Softw Tools Technol Transfer

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Abstract. We study price-per-reward games on hybrid automata with strong resets. They generalise priced games previously studied and have applications in scheduling. We obtain decidability results by a translation to a novel class of finite graphs with price and reward information, and games assigned to edges. The cost and reward of following an edge are determined by the outcome of the edge game that is assigned to it.

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On O-Minimal Hybrid Systems

Cited by 36 publications

References 14 publications

Decidable Compositions of O-Minimal Automata

Decidable Compositions of O-Minimal Automata

Reachability Problems on Extended O-Minimal Hybrid Automata

Average-price-per-reward games on hybrid automata with strong resets

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