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Page 3789 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
Corollary: There exists no minimal isomorphically complete system of finite automata with respect to the v-product (i> 1).  ...  Theorem 1: A system = of finite automata is isomorphically complete with respect to the v,-product (i> 1) if and only if for any n>1 there exists an & E> such that D,, can be isomorphically embedded into  ... 

Finite isomorphically complete systems

F. Gécseg, B. Imreh
1992 Discrete Applied Mathematics  
Let us suppose that a finite system f of finite automata is isomorphically complete with respect to the g-product.  ...  In this paper we show that the existence of finite complete systems implies the unboundedness of the feedback dependency of the composition.  ...  Moreover, let T be a oneto-one mapping of B into S. Now define the functions  ... 
doi:10.1016/0166-218x(92)90261-8 fatcat:q6cgshxyerhrhnbobcoqb4bbki

Page 8776 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
Alexandra Kireeva (Dudweiler) 99m:68131 68Q70 Gécseg, Ferenc (H-SZEG-C; Szeged); Imreh, Balazs (H-SZEG-C; Szeged) ; Pluhar, Andras (H-SZEG-C; Szeged) On the existence of finite isomorphically complete  ...  Under the isomor- phic embedding as representation, a graph-theoretical necessary condition for the existence of finite complete systems was pre- sented in [F. Gécseg and B. Imreh, Discrete Appl.  ... 

Page 3631 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
The result extends a result of the authors on finite isomorphically complete systems in the theory of finite automata [Discrete Appl. Math. 36 (1992), no. 3, 307-311; MR 93b:68055]. K. G.  ...  The authors give necessary conditions under which there exist finite 68Q Theory of computing 95f:68128 isomorphically complete systems of tree automata with respect to a suitable composition, for a given  ... 

Page 337 of Mathematical Reviews Vol. , Issue 83a [page]

1983 Mathematical Reviews  
A system = of automata is said to be isomorphically complete for 8 with respect to the a-product if any automaton from % can be embedded isomorphically into an a-product of automata from =.  ...  sufficient conditions are given for a system of automata to be isomorphically complete for ® with respect to the a-product (Theorem 2).  ... 

Page 1593 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
Denoting the class of all tree automata with rank-type R by Zz and the class of all nilpotent tree automata by “Zp, they define the notion of a subset Y of Zp being an isomorphically complete system for  ...  Their main result is a necessary and sufficient condition for a system of tree automata to have the property of being isomorphically complete for Wp with respect to a;-products.  ... 

Automata in the Category of Glued Vector Spaces [article]

Thomas Colcombet, Daniela Petrişan
2017 arXiv   pre-print
The main instantiation of our construction is a new class of automata that are hybrid between deterministic automata and automata weighted over a field.  ...  In this paper we adopt a category-theoretic approach to the conception of automata classes enjoying minimization by design.  ...  it comes the existence of minimal automata.  ... 
arXiv:1711.06065v1 fatcat:giecpkz3uneuxeeknggkfjgy2q

Page 3873 of Mathematical Reviews Vol. , Issue 83i [page]

1983 Mathematical Reviews  
{For the entire collection see MR 83b:68001a. } S. M. Goberstein (Chico, Calif.) Déomisi, P. 831:68088 On homomorphically qd-complete systems of finite automata.  ...  Authors’ summary: “Using a pair of finite-state automata to model the transmitter-receiver protocol in a data communications system, we derive lower bounds on the size of automata needed to achieve reliable  ... 

Page 4721 of Mathematical Reviews Vol. , Issue 84k [page]

1984 Mathematical Reviews  
is A-complete if and only if it does not belong as a whole to one of the sets of system S$.” { For the entire collection see MR 84c:68002.}  ...  4721 Author’s introduction: “We consider the function system P whose elements are mappings realizable by finite automata (boundedly-determined or BD functions) and by the operations of superposition and  ... 

Page 2925 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
More results by the same authors on n-complete automata networks, and on finite automata networks in general, can be found in their fundamental work [Math.  ...  Introduction: “The investigation of homomorphic or isomorphic embeddings into products of automata is the starting point in the study of homomorphic or isomorphic completeness of certain classes of automata  ... 

Page 1205 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
This characterization implies the existence of fi- nite isomorphically complete systems of nondeterministic tree au- tomata with respect to the Glushkov-type product.  ...  He defines a Glushkov-type product of such automata and char- acterizes the isomorphically complete systems with respect to the composition.  ... 

Page 1069 of Mathematical Reviews Vol. , Issue 88b [page]

1988 Mathematical Reviews  
The main problems solved in this monograph (sometimes only partially) are (1) the characterization of complete systems of automata, (2) the existence of minimal complete systems, and (3) the comparison  ...  On the basis of the presentation semantics, a complete (semiformal) proof system for specifications is derived.  ... 

Page 1175 of Mathematical Reviews Vol. , Issue 85c [page]

1985 Mathematical Reviews  
Watanabe, Toshimasa (J-HROSE-A); 85c:68056 Nakamura, Akira (J-HROSE-A) On the transformation semigroups of finite automata. J. Comput. System Sci. 26 (1983), no. 1, 107-138.  ...  The authors also show the relationship between partial and total abstract types, “establish a sound and complete proof system, and give sufficient (syntactic) conditions for the existence of initial and  ... 

Page 2583 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
criterion; a class of finite automata is complete with respect both to homomorphic and isomorphic simulations under the a@-v3-product iff it has this property under the general (Glushkov-type) product.  ...  The author presents a survey on expressiveness and complete- ness of iterative automaton algebras.  ... 

Page 6994 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
Therefore, classes of finite automata that are also complete with respect to homomorphic representation are also complete with respect to both homomorphic and isomorphic simulations, and vice versa.”  ...  In more detail, we prove that a class of finite automata is complete with respect to both ho- momorphic and isomorphic simulations if and only if it satisfies Letichevskii’s criterion.  ... 
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