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On the equivalence of the cube-product and the general product of automata

B. Imreh
2000 Theoretical Computer Science  
In this work it is shown that the general product is equivalent to the cube-product with respect to the isomorphic representation.  ...  Using this equivalence we characterize the homomorphically complete systems of automata with respect to the cube-product.  ...  The general product of nondeterministic tree automata is equivalent to the cube-product of nondeterministic tree automata with respect to the isomorphic representation. Corollary 7 (Imreh [13] ).  ... 
doi:10.1016/s0304-3975(99)00276-5 fatcat:ipj577iwbvd45ofizl5plmp5qy

Page 2884 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
isomorphic representations of monotone tree and nondeterministic tree automata.  ...  First, the isomorphically complete systems of tree automata for the class of monotone tree automata are characterized with respect to the ao-product.  ... 

Page 6996 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
This notion leads to the notions of isomorphically complete and of homomorphically complete systems of nondeterministic automata. The main results of the paper are two theorems.  ...  The first of them presents a necessary and sufficient condition for a system of nondeterministic automata to be isomorphically complete with respect to the general product.  ... 

Page 7775 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
We show that a tree automaton is definite if and only if it can be ho- momorphically or isomorphically represented by a cascade com- position of two-state reset tree automata.”  ...  7775 responding to A is a direct sum of pairwise isomorphic strongly connected right group-type quasi-automata.  ... 

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

1997 Mathematical Reviews  
Homomorphic and isomorphic simulations of automata are stud- ied.  ...  nondeterministic finite automata.  ... 

Page 5587 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
In this work we deal with the isomorphic representation of nondeterministic automata with respect to the cube-product intro- duced for deterministic automata in a paper by Imreh [in Words, languages and  ...  {For Part I see the preceding review. } 96i:68061 68Q75 68Q70 Gécseg, Ferenc (H-SZEG-C; Szeged); Imreh, Balazs (H-SZEG-C; Szeged) On the cube-product of nondeterministic automata.  ... 

Cumulative subject index volumes 68–71

1986 Information and Control  
, probabilistic analysis, 68, 47 optimally data-efficient, for isomorphism inference:  ...  Aggregation problems, formulation of several versions, analysis from recursion theoretic point of view, 70, 69 Algorithms for circular retrieval and k-nearest neighbor search problems, description and  ...  single worktape Turing machines, 70, 179 Trees game, associated problems, solution on interconnected processor array, 69, 168 Turing machines nondeterministic single worktape: simultaneous relations  ... 
doi:10.1016/s0019-9958(86)80014-6 fatcat:hkligygazvcyvdgrhtvhrefpj4

Page 1978 of Mathematical Reviews Vol. , Issue 80E [page]

1980 Mathematical Reviews  
union, intersection, concatenation, Kleene closure, reversal, or e-free ho- momorphism.” 80e:68153 Reisig, Wolfgang A note on the representation of finite tree automata.  ...  and non-order-theoretic fixed point models for iteration.” 80e:68 150 Mikolajezak, B. 80e:68 151 On the isomorphisms of generalized finite automata extensions and generalized periodic sums.  ... 

Page 7079 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
Summary: “In this paper, we characterize the isomorphically com- plete systems of nondeterministic tree automata with respect to the family of a;-products.  ...  (H-SZEG-I; Szeged) On a;-products of nondeterministic tree automata. (English summary) Acta Cybernet. 13 (1997), no. 1, 41-54.  ... 

Page 3414 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
However, the minimal realizations of a deterministic tree transducer are not isomorphic.  ...  We investigate conditions assuring the uniqueness (up to isomorphism) of minimal realizations in certain classes of tree transducers.  ... 

Page 2944 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
Pokrovskaya (RZhMat 1981:12 V940) Peak, I. 83g:68082 On a common representation of some semigroups of Mealy-automata. Papers on automata theory, IT, pp. 1-12, DM 80, 5, Karl Marx Univ.  ...  ), where the input tapes of these automata are restricted to cubic ones.  ... 

Page 7116 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
The author presents two transformations: from alternating into nondeterministic Biichi automata, and from formulas of propo- sitional temporal logic into alternating Biichi automata.  ...  Cazdnescu (Bucharest) 97k:68118 68Q68 03D05 68Q60 Isli, Amar (F-PARIS13-GI; Villetaneuse) Converting a Biichi alternating automaton to a usual nondeterministic one.  ... 

Page 336 of Mathematical Reviews Vol. , Issue 83a [page]

1983 Mathematical Reviews  
Tree-size on ATMs is shown to correspond closely to time on nondeterministic TMs and on nondeterministic auxiliary pushdown automata.  ...  {Japanese original: Denshi Tsushin Gakkai Ronbunshi D 62 (1979), no. 7, 475-482. } Imreh, B. 83a:68072 On isomorphic representations of commutative automata with respect to a,-products.  ... 

Version Space Algebras are Acyclic Tree Automata [article]

James Koppel
2021 arXiv   pre-print
We present a linear-time semantics-preserving constructive embedding from version space algebras into nondeterministic finite tree automata, showing that the former are but a special case of the latter  ...  Combined with recent results finding a correspondence between e-graphs and minimal deterministic tree automata, this shows that tree automata are strict generalizations of all recent major approaches to  ...  The grammar of normalized VSAs is: := (P( ) 1 , . . . , P( ) ) P( ) := U U U ( 1 , . . . , ) Bottom-up) Nondeterministic Finite Tree Automata (NFTA)).  ... 
arXiv:2107.12568v1 fatcat:7mhjl7lnufckpfhtkwlyrztvgi

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

2000 Mathematical Reviews  
Alexandra Kireeva (Dudweiler) 2000d:68101 68Q70 Székely, Ildiko (H-SZEG-C; Szeged) Isomorphic representation of nondeterministic nilpotent automata.  ...  “In this paper, we generalize the notion of nilpotency for nonde- terministic automata and study the isomorphic representation of nondeterministic nilpotent automata under the direct product.  ... 
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