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Characteristic Semigroups of Directable Automata [chapter]

Tatjana Petković, Miroslav Ćirić, Stojan Bogdanović
2003 Lecture Notes in Computer Science  
The properties of these, so-called characteristic, semigroups are studied and semigroups that can be characteristic semigroups of directable automata are characterized.  ...  This is the motivation for assigning a new kind of semigroups to directable automata, which is done in this paper.  ...  Also, we describe semigroups that can be characteristic semigroups of some directable automata.  ... 
doi:10.1007/3-540-45005-x_37 fatcat:rvdzox4tdfgvnbcgcgax2mzf2q

Page 1907 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
In Section | we give a new description of the characteristic semigroups of Mealy automata by pairs of mappings.  ...  Hoehnke (Berlin) Dang Huu Dao 83e:20078a *On the characteristic semigroups of Mealy automata and on a problem of I. Peak. DM 79, 1.  ... 

The amalgamation of automata

Toshimasa Watanabe, Shoichi Noguchi
1977 Journal of computer and system sciences (Print)  
We demonstrate in this paper a direct product decomposability of automata, and discuss the hierarchy of automata which is characterized by the characteristic semigroups.  ...  By introducing the concept of the amalgamation of automata, we discuss their structure and classification in terms of characteristic semigroups, when the input is a free semigroup generated by a set of  ...  Let ~ = [~i=l.k ~[o, Direct Product and Amalgamation of Automata A direct product of automata is defined in this section, and it is shown that the characteristic semigroup of a direct product of automata  ... 
doi:10.1016/s0022-0000(77)80024-x fatcat:hhtnwww2tfc25lamx2nguluhuy

Some remarks on the π-directable automata and definite automata: A survey

Milena Bogdanovic
2015 Godisnjak Uciteljskog fakulteta u Vranju  
The concept of π-directable automata is a concomitant specialization concept of the directable automata and generalization of the concept definite automata.  ...  The main purpose of this survey is to describe certain properties of πdirectable and definite automata.  ...  Theorems that follow provide a variety of characteristics of -directable automata. Theorem 2.4.  ... 
doi:10.5937/gufv1506083b fatcat:a2myu5w4tjcqpapufefoy4wklq

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

1983 Mathematical Reviews  
The author proves a couple of theorems relating state independence to the characteristic semigroup of a Mealy machine and to a modified direct product of Mealy machines.  ...  Dang Huu Dao 831:68087 Further results on characteristic semigroups of Mealy-automata. Papers on automata theory, I, pp. 47-78, DM 80, 2, Karl Marx Univ. Econom., Budapest, 1980.  ... 

Page 2818 of Mathematical Reviews Vol. , Issue 93e [page]

1993 Mathematical Reviews  
(iv) The simple Mealy automaton 4 is characteristically output- free if and only if there is a subautomaton of A such that it is a direct sum of isomorphic characteristically output-free Mealy automata  ...  (iii) The characteristic semigroup of a simple output-independent Mealy automaton is left cancellative.  ... 

Page 2099 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
The cardinality of characteristic semigroups of automata is dis- cussed.  ...  Assuming that r = 2, this paper gives the exact cardinality or upper bound of characteristic semigroups of such automata as direct sums of and direct products of some strongly connected au- tomata and  ... 

Page 8172 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
of automata.  ...  Directability of nondeterministic (n.d.) automata can be defined in different ways. In [B. Imreh and M.  ... 

Finite semigroups, feedback, and the Letichevsky criteria on non-empty words in finite automata

Pál Dömösi, Chrystopher L. Nehaniv, John L. Rhodes
2003 Theoretical Computer Science  
The latter two cases are exactly the cases in which the characteristic semigroup is ¡ -trivial.  ...  , to the following properties of the characteristic semigroup of the automaton: (1) non-constructability as a divisor of a cascade product of copies of the two-element monoid with zero , (2) such constructability  ...  In particular, the characteristic semigroup of the right regular representation ¦ q Þ © h is , and moreover, the characteristic semigroup r¦ q£ V o of £ V is just the characteristic semigroup r¦ q£ of  ... 
doi:10.1016/s0304-3975(02)00848-4 fatcat:rhar6ye3lfhnjhmmv4xrx5fqmm

Algebraic Hierarchical Decomposition of Finite State Automata: Comparison of Implementations for Krohn-Rhodes Theory [chapter]

Attila Egri-Nagy, Chrystopher L. Nehaniv
2005 Lecture Notes in Computer Science  
The hierarchical algebraic decomposition of finite state automata (Krohn-Rhodes Theory) has been a mathematical theory without any computational implementations until the present paper, although several  ...  We represent a semigroup by a set of generators (the transformations induced by the input symbols of the automaton) instead of by a Cayley-table, finite presentation, or explicit enumeration of all elements  ...  Therefore the standard V ∪ T technique cannot be used for practical purposes: due to its redundancy it may produce even more components than the order of the characteristic semigroup (e.g. the full transformation  ... 
doi:10.1007/978-3-540-30500-2_32 fatcat:dgwpvmxztfgttfn7jhw54e3ycy

Characterization of state-independent automata

Jerzy W. Grzymala-Busse, Zamir Bavel
1986 Theoretical Computer Science  
The class ofall state-independent au)omata is characterized as a subclass of all semigroup automata (automata generated by semigroups).  ...  A state-independent automaton is identified as an automaton over a finite semigroup that is stationary on the fight. Associated results are included. amtn~ ~hm~m~ 0304-3975/86/$3.50  ...  We can thus define a state-independent automaton (Q, J) as a semigroup Q that is right stationary.  ... 
doi:10.1016/0304-3975(86)90162-3 fatcat:hl2sf7wlwfbdhmhrvkrrwppoua

Page 2335 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
Further, semigroup automata are studied; an automaton @=(A,X,8) is a semigroup automaton if A = X=S, where S is a semigroup, and 8(s,s’) = s-s’ (the product in S).  ...  Each RG-lattice decomposes into a direct sum of indecomposable lattices, uniquely up to isomorphism and order of occurrence of the summands.  ... 

Page 2883 of Mathematical Reviews Vol. , Issue 84g [page]

1984 Mathematical Reviews  
This paper continues the work of Dang Huu Dao [On the characteristic semigroups of Mealy automata and on a problem of I. Péak, see pp. 37-53, Karl Marx Univ. Econom., Dept.  ...  The Moore and quasi-Moore semigroups for the classes of commutative, nilpotent, definite, combinatorial, directable and locally testable automata are characterized.  ... 

Page 1657 of Mathematical Reviews Vol. 57, Issue 5 [page]

1979 Mathematical Reviews  
type semigroup over a field of dimension N and ; is an integer in [0, N], there exists for the class Y, of the characteristic groups of H, of dimension j, a finiteness measure computed by the subroutine  ...  As a direct conse- quence, we prove the “Burnside theorem’”’ for matrix semigroups over a commutative field; another proof is due to R. McNaughton and Y.  ... 

Page 359 of Mathematical Reviews Vol. 57, Issue 1 [page]

1979 Mathematical Reviews  
To every direct decomposition FE, ® --- @ E, of the endomorph- ism semigroup of a characteristically free quasi-automaton A, we can construct an A-direct decomposition A; ® --- @A, of A such that E(A,)  ...  element of the characteristic semigroup F“ of A represented by f.  ... 
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