Automata with Group Actions

Bojańczyk, Mikołaj; Klin, Bartek; Lasota, Sławomir

doi:10.1109/lics.2011.48

Cited by 65 publications

(105 citation statements)

References 11 publications

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“…This was shown in [3] for least supports and Cartesian products, and in [4] for orbit refinement. For other examples of data symmetries that satisfy these properties, see [3,4].…”

Section: Assumptions On the Data Symmetrymentioning

confidence: 76%

“…Unlike the conference version, we use the more general notion of nominal sets, from [3], which allows more structure on data values, such as order instead of equality only.…”

Section: Progress Beyond the Conference Versionmentioning

confidence: 99%

“…Background The definition of nominal sets presented above is based on, but not identical to, the one from [3]. The definition used in this paper is slightly more relaxed than the one in [3]; in [3] the category of nominal sets used only equivariant sets and equivariant objects.…”

Section: Assumptions On the Data Symmetrymentioning

confidence: 99%

“…The definition used in this paper is slightly more relaxed than the one in [3]; in [3] the category of nominal sets used only equivariant sets and equivariant objects. The difference between the nominal sets from [3] and this paper, and the nominal sets of Gabbay and Pitts [7], is that here and in [3] there is the additional parameter of a data symmetry, while in [7] the data symmetry is always assumed to be the same, namely D is the natural numbers and G is the set of all permutations of natural numbers.…”

Section: Assumptions On the Data Symmetrymentioning

confidence: 99%

See 3 more Smart Citations

Nominal Monoids

Bojańczyk

2013

Theory Comput Syst

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“…This was shown in [3] for least supports and Cartesian products, and in [4] for orbit refinement. For other examples of data symmetries that satisfy these properties, see [3,4].…”

Section: Assumptions On the Data Symmetrymentioning

confidence: 76%

“…Unlike the conference version, we use the more general notion of nominal sets, from [3], which allows more structure on data values, such as order instead of equality only.…”

Section: Progress Beyond the Conference Versionmentioning

confidence: 99%

Section: Assumptions On the Data Symmetrymentioning

confidence: 99%

Section: Assumptions On the Data Symmetrymentioning

confidence: 99%

See 2 more Smart Citations

Nominal Monoids

Bojańczyk

2013

Theory Comput Syst

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“…Recent work on the quantitative analysis of programs [5] also uses weighted automata, but does not deal with minimization or with notions of regularity. Data languages [7] are concerned with strings over a (possibly infinite) data domain D. Recent models [3] have obtained Myhill-Nerode characterizations, and hence minimization algorithms, but the models are intended as acceptors, and not for computing more general functions. Turn-based weighted games [9] are ACRA games with a single register, and in this special setting, it is possible to solve non-negative optimal reachability in polynomial time.…”

Section: Introductionmentioning

confidence: 99%

Decision Problems for Additive Regular Functions

Alur

Raghothaman

2013

Automata, Languages, and Programming

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Abstract. Additive Cost Register Automata (ACRA) map strings to integers using a finite set of registers that are updated using assignments of the form "x := y + c" at every step. The corresponding class of additive regular functions has multiple equivalent characterizations, appealing closure properties, and a decidable equivalence problem. In this paper, we solve two decision problems for this model. First, we define the register complexity of an additive regular function to be the minimum number of registers that an ACRA needs to compute it. We characterize the register complexity by a necessary and sufficient condition regarding the largest subset of registers whose values can be made far apart from one another. We then use this condition to design a pspace algorithm to compute the register complexity of a given ACRA, and establish a matching lower bound. Our results also lead to a machine-independent characterization of the register complexity of additive regular functions. Second, we consider two-player games over ACRAs, where the objective of one of the players is to reach a target set while minimizing the cost. We show the corresponding decision problem to be exptime-complete when the costs are non-negative integers, but undecidable when the costs are integers.

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A Myhill-Nerode Theorem for Register Automata and Symbolic Trace Languages

Vaandrager

Midya

2020

Theoretical Aspects of Computing – ICTAC 2020

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This publication is distributed under the terms of Article 25fa of the Dutch Copyright Act (Auteurswet) with explicit consent by the author. Dutch law entitles the maker of a short scientific work funded either wholly or partially by Dutch public funds to make that work publicly available for no consideration following a reasonable period of time after the work was first published, provided that clear reference is made to the source of the first publication of the work. This publication is distributed under The Association of Universities in the Netherlands (VSNU) 'Article 25fa implementation' pilot project. In this pilot research outputs of researchers employed by Dutch Universities that comply with the legal requirements of Article 25fa of the Dutch Copyright Act are distributed online and free of cost or other barriers in institutional repositories. Research outputs are distributed six months after their first online publication in the original published version and with proper attribution to the source of the original publication.You are permitted to download and use the publication for personal purposes. Please note that you are not allowed to share this article on other platforms, but can link to it. All rights remain with the author(s) and/or copyrights owner(s) of this work. Any use of the publication or parts of it other than authorised under this licence or copyright law is prohibited. Neither Radboud University nor the authors of this publication are liable for any damage resulting from your (re)use of this publication.If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the ma terial

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Automata with Group Actions

Cited by 65 publications

References 11 publications

Nominal Monoids

Nominal Monoids

Decision Problems for Additive Regular Functions

A Myhill-Nerode Theorem for Register Automata and Symbolic Trace Languages

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