Quantitative simulations by matrices

Urabe, Natsuki; Hasuo, Ichiro

doi:10.1016/j.ic.2016.03.007

Cited by 7 publications

(24 citation statements)

References 52 publications

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“…In this context our unique standing is in the emphasis on automatic verification algorithms. For example, in [84,86] we introduced matrix simulations, a probabilistic notion we obtained via a coalgebraic generalization of conventional simulations from [64]. It is demonstrated in [84,86] that they allow effective algorithmic search by linear programming.…”

Section: Metamathematical Transfer Example Ii: From Automata To Coalmentioning

confidence: 99%

“…For example, in [84,86] we introduced matrix simulations, a probabilistic notion we obtained via a coalgebraic generalization of conventional simulations from [64]. It is demonstrated in [84,86] that they allow effective algorithmic search by linear programming. Through this work and others [85,86] we are now convinced of the following coalgebraic unfolding scheme (Fig.…”

Section: Metamathematical Transfer Example Ii: From Automata To Coalmentioning

confidence: 99%

“…It is demonstrated in [84,86] that they allow effective algorithmic search by linear programming. Through this work and others [85,86] we are now convinced of the following coalgebraic unfolding scheme (Fig. 8): Table 4 Notions around system dynamics formulated in categorical terms -For many formal methods problems, the key is to unfold complex structures and reduce them to (structurally) simpler, well-known problems such as satisfiability (SAT), linear programming (LP) and semidefinite programming (SDP, a wellknown class of nonlinear convex optimization problems).…”

Section: Metamathematical Transfer Example Ii: From Automata To Coalmentioning

confidence: 99%

“…one-way bisimulation). It is our contribution in [86] to exploit our coalgebraic characterization of simulation [39] and formulate quantitative simulation in terms of matrices. The latter notion of quantitative simulation allows efficient search by linear programming, see Fig.…”

Section: Simulation and Bisimulation Notionsmentioning

confidence: 99%

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Metamathematics for Systems Design

Hasuo

2017

New Gener. Comput.

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This position paper describes the context, the goal, the strategy and the tactics of the ERATO MMSD project (2016-2022. The project aims at enhanced quality assurance measures for industry products like cars. In doing so, we follow a recent trend and exploit formal methods, a body of mathematical techniques originally developed for computer systems. However, there are fundamental gaps in application of formal methods to industry products: additional concerns in industry products such as continuous dynamics of physical components and quantitative measures such as probability, time, and cost make problems fundamentally different from those about software. Formal methods that accommodate these concerns is an active research area, which shows that it is a hard problem. There are several successful theoretical developments in this direction. They typically combine one individual technique with one specific concern, such as hybrid automata that extend automata with continuous dynamics. Our project aims to contribute to this hard problem in a unique way. In our project we will take a unique metamathematical strategy to bridging the gaps: instead of creating one technique for each concern, we want to find a meta-level theory that describes how to develop such techniques for many potential concerns in general. Through this strategy, together with our emphasis on real-world applications in industry, we expect a new prototype of applied mathematics will emerge. In this prototype, abstraction and genericitycharacteristics of modern mathematics that are not often associated with application-are turned into crucial advantages in applications.

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Section: Metamathematical Transfer Example Ii: From Automata To Coalmentioning

confidence: 99%

Section: Metamathematical Transfer Example Ii: From Automata To Coalmentioning

confidence: 99%

Section: Metamathematical Transfer Example Ii: From Automata To Coalmentioning

confidence: 99%

Section: Simulation and Bisimulation Notionsmentioning

confidence: 99%

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Metamathematics for Systems Design

Hasuo

2017

New Gener. Comput.

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“…Simulations-as one-step, local witnesses for trace inclusion-have been often used as a sound (but not necessarily complete) proof method that is computationally more tractable; with the observations in [31] we are naturally interested in them. Possible directions are: synthesis of simulation matrices between finite systems by linear programming, like in [30]; synthesis of simulations by other optimization techniques for program verification (where problem instances are infinite due to the integer type); and simulations as a proof method in interactive theorem proving.…”

Section: Future Workmentioning

confidence: 99%

Coalgebraic Trace Semantics for Buechi and Parity Automata

Urabe

Shimizu

Hasuo

2016

Preprint

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Despite its success in producing numerous general results on state-based dynamics, the theory of coalgebra has struggled to accommodate the Büchi acceptance condition-a basic notion in the theory of automata for infinite words or trees. In this paper we present a clean answer to the question that builds on the "maximality" characterization of infinite traces (by Jacobs and Cîrstea): the accepted language of a Büchi automaton is characterized by two commuting diagrams, one for a least homomorphism and the other for a greatest, much like in a system of (least and greatest) fixed-point equations. This characterization works uniformly for the nondeterministic branching and the probabilistic one; and for words and trees alike. We present our results in terms of the parity acceptance condition that generalizes Büchi's.

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