Theory of Automata

Ginzburg, Abraham

doi:10.1016/0016-0032(71)90064-0

Cited by 17 publications

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“…This condition is satisfied in some cases of practical interest, such as the shortest path problem in a graph (possibly with negative weights) and its multimensional equivalents. Here our algorithm becomes the well-known Floyd algorithm [13].…”

Section: Introductionmentioning

confidence: 99%

Networks of constraints: Fundamental properties and applications to picture processing

Montanari

1974

Information Sciences

976

459

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The problem of representation and handling of constraints is here considered, mainly for picture processing purposes. A systematic specification and utilization of the available constraints could significantly reduce the amount of search in picture recognition. On the other hand, formally stated constraints can be embedded in the syntactic productions of picture languages.Only binary constraints are treated here, but they are represented in full generality as binary relations. Constraints among more than two variables are then represented as networks of simultaneous binary relations. In general, more than one equivalent (i.e., representing the same constraint) network can be found: a minimal equivalent network is shown to exist, and its computation is shown to solve most practical problems about constraint handling.No exact solution for this central problem was found. Anyway, constraints are treated algebtaically, and the solution of a system of linear equations in this algebra provides an approximation of the minimal network. This solution is then proved exact in special cases, e.g., for tree-like and series parallel networks and for classes of relations for which a distributive property holds. This latter condition is satisfied in cases of practical interest.

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Section: Introductionmentioning

confidence: 99%

Networks of constraints: Fundamental properties and applications to picture processing

Montanari

1974

Information Sciences

976

459

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“…Among the numerous proofs of the Krohn-Rhodes primary decomposition theorem those of Zeiger [15,16] were more automata oriented. Zeiger's proof has been corrected and presented more clearly in Ginzburg's book [2] based on some constructs attributed to Yoeli [14]. Ginzburg's proof Fig.…”

Section: Discussionmentioning

confidence: 99%

“…The proof in [2] inspired Eilenberg to give a slight generalization of the primary decomposition, the holonomy decomposition ( [1], pp. 43-50).…”

Section: Discussionmentioning

confidence: 99%

“…The theorem states that any automaton, up to homomorphism, can be realized by a cascade of elementary automata of two types, permutation automata where each letter induces a permutation of the state space, and reset automata where each letter is either a reset (sends all states to a fixed single state) or an identity (a self-loop from every state). However, as noted in the last paragraph of [2] "Finally, notice that the above theory does not indicate how many particular basic building blocks are needed to construct a cascade product covering of a given semiautomaton." I had the privilege to discuss the topic with the late Marcel-Paul Schützenberger who encouraged me to look at the holonomy decomposition theorem, a variant of the KrohnRhodes theorem, written on eight dense pages of volume B of Eilenberg's book [1] to which he contributed.…”

Section: Introductionmentioning

confidence: 99%

“…Fortunately, the book of Ginzburg [2] gave a clear automata-theoretic presentation from which one could understand that a cascade of automata is a particular type of composition where the automata are ordered and each automaton reads the common input alphabet and the states of its preceding automata or, equivalently, the output of its predecessor, as illustrated in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

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On the Krohn-Rhodes Cascaded Decomposition Theorem

Maler

2010

Time for Verification

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Dedicated to the memory of Amir Pnueli, deeply missed.Abstract. The Krohn-Rhodes theorem states that any deterministic automaton is a homomorphic image of a cascade of very simple automata which realize either resets or permutations. Moreover, if the automaton is counter-free, only reset automata are needed. In this paper we give a very constructive proof of a variant of this theorem due to Eilenberg.

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Radhakrishnan¹

2007

Bell Labs Tech. J.

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IP Multimedia Subsystem (IMS) solutions emphasize services including allInternet Protocol (IP) voice, data, video, multimedia, and other user-centric technologies-make possible such interactive multimedia services as multiparty video conference and user mobility (presence and location management) [15]. These services are the major contributors to data diversity in the network.Services operate on network and subscriber data in the network. Collectively, the network contains enormous amounts of service data. The structure (relational, hierarchical) and the kind (voice, video, text) of data depend on the service and technology, such as wireline or Voice over IP (VoIP). The diversity of data, services, technology, and vendors has caused the proliferation of provisioning systems, each catering to a technology domain [12] or a vendor [9] or a class of service [14]. These differences pose many challenges to unification. In literature,

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Theory of Automata

Cited by 17 publications

References 0 publications

Networks of constraints: Fundamental properties and applications to picture processing

Networks of constraints: Fundamental properties and applications to picture processing

On the Krohn-Rhodes Cascaded Decomposition Theorem

Provisioning in complex networks

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