University of Hertfordshire Research Archive

        JavaScript is disabled for your browser. Some features of this site may not work without it.

        Browse

        All of UHRABy Issue DateAuthorsTitlesThis CollectionBy Issue DateAuthorsTitles

        Arkivum Files

        My Downloads
        View Item 
        • UHRA Home
        • University of Hertfordshire
        • Research publications
        • View Item
        • UHRA Home
        • University of Hertfordshire
        • Research publications
        • View Item

        Symmetries of Automata

        View/Open
        Published_Version.pdf (PDF, 659Kb)
        Author
        Egri-Nagy, Attila
        Nehaniv, C.L.
        Attention
        2299/16515
        Abstract
        For a given reachable automaton A, we prove that the (state-)endomorphism monoid End(A) divides its characteristic monoid M(A). Hence so does its (state-)automorphism group Aut(A), and, for finite A, Aut(A) is a homomorphic image of a subgroup of the characteristic monoid. It follows that in the presence of a (state-) automorphism group G of A, a finite automaton A (and its transformation monoid) always has a decomposition as a divisor of the wreath product of two transformation semigroups whose semigroups are divisors of M(A), namely the symmetry group G and the quotient of M(A) induced by the action of G. Moreover, this division is an embedding if M(A) is transitive on states of A. For more general automorphisms, which may be non-trivial on input letters, counterexamples show that they need not be induced by any corresponding characteristic monoid element.
        Publication date
        2015-03-24
        Published in
        Algebra and Discrete Mathematics
        Other links
        http://hdl.handle.net/2299/16515
        Metadata
        Show full item record
        Keep in touch

        © 2019 University of Hertfordshire

        I want to...

        • Apply for a course
        • Download a Prospectus
        • Find a job at the University
        • Make a complaint
        • Contact the Press Office

        Go to...

        • Accommodation booking
        • Your student record
        • Bayfordbury
        • KASPAR
        • UH Arts

        The small print

        • Terms of use
        • Privacy and cookies
        • Criminal Finances Act 2017
        • Modern Slavery Act 2015
        • Sitemap

        Find/Contact us

        • T: +44 (0)1707 284000
        • E: ask@herts.ac.uk
        • Where to find us
        • Parking
        • hr
        • qaa
        • stonewall
        • AMBA
        • ECU Race Charter
        • disability confident
        • AthenaSwan