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Characteristic Semigroups of Directable Automata
[chapter]

2003
*
Lecture Notes in Computer Science
*

The properties

doi:10.1007/3-540-45005-x_37
fatcat:rvdzox4tdfgvnbcgcgax2mzf2q
*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*. ...##
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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. ...##
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The amalgamation of automata

1977
*
Journal of computer and system sciences (Print)
*

We demonstrate in this paper a

doi:10.1016/s0022-0000(77)80024-x
fatcat:hhtnwww2tfc25lamx2nguluhuy
*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*...##
###
Some remarks on the π-directable automata and definite automata: A survey

2015
*
Godisnjak Uciteljskog fakulteta u Vranju
*

The concept

doi:10.5937/gufv1506083b
fatcat:a2myu5w4tjcqpapufefoy4wklq
*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*π*directable*and definite*automata*. ... Theorems that follow provide a variety*of**characteristics**of*-*directable**automata*. Theorem 2.4. ...##
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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. ...##
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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. ...

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

2003
*
Theoretical Computer Science
*

The latter two cases are exactly the cases in which the

doi:10.1016/s0304-3975(02)00848-4
fatcat:rhar6ye3lfhnjhmmv4xrx5fqmm
*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*...##
###
Algebraic Hierarchical Decomposition of Finite State Automata: Comparison of Implementations for Krohn-Rhodes Theory
[chapter]

2005
*
Lecture Notes in Computer Science
*

The hierarchical algebraic decomposition

doi:10.1007/978-3-540-30500-2_32
fatcat:dgwpvmxztfgttfn7jhw54e3ycy
*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 ...##
###
Characterization of state-independent automata

1986
*
Theoretical Computer Science
*

The class ofall state-independent au)omata is characterized as a subclass

doi:10.1016/0304-3975(86)90162-3
fatcat:hl2sf7wlwfbdhmhrvkrrwppoua
*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. ...##
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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. ...##
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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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