Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Article type: Research Article
Authors: Janicki, Sławomira | Szynal, Dominika
Affiliations: [a] College of Engineering of Lublin, Institute of Mathematics, Maria Curie-Skłodowska University, Lublin
Abstract: There are a great many research works concerning the well-known stochastic automata of Moore, Mealy, Rabin, Turing and others. Recently an automaton of Markov’s chain type has been introduced by Bartoszyński. This automaton is obtained by a generalization of Pawlak’s deterministic machine. The aim of this note is to give a concept of a stochastic automaton of Markov’s generalized chain type. The introduced automaton called a stochastic k-automaton (s.k-a.) is a common generalization of Bartoszyński’s automaton and Grodzki’s deterministic k-machine. By a stochastic k-automaton we mean an ordered triple Mk=⟨U,a,π⟩, k⩾1, where U denotes a finite non-empty set, a is a function from Uk to [0, 1] with ∑v∈Uka(v)=1, and π is a function from Uk+1 to [0,1] with ∑u∈Uπ(v,u)=1 for every v∈Uk. For all N⩾k we can define a probability measure PN on UN=U×U×…×U as follows: PN(u1,u2,…,uN)=a(u1,u2,…,uk)π(u1,u2,…,uk+1)π(u2,u3,…,uk+2)…π(uN−k,uN−k+1,…,uN). We deal with the problems of the shrinkage and the extension of a system of s.k-a.’s Mk(i)=⟨U,a(i),π(i)⟩, i=1,2,…,m,m⩾2. In this note there are given conditions under which an s.k-a. Mk=⟨U,a,π⟩ exists and the language of this automaton defined as LM={(u1,u2,u3,…):∧N⩾1PN(ul,u2,…uN)>0} either contains the languages of all the automata Mk(i),i=1,2,…,m, or this language equals the intersection of all those languages.
Keywords: stochastic k-automaton, extension, shrinkage, N-word, set of N-words, words, language, probability measure, carrier, concordance, truly concordance, pairwise concordance
DOI: 10.3233/FI-1977-1114
Journal: Fundamenta Informaticae, vol. 1, no. 1, pp. 231-241, 1977
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
USA
Tel: +1 703 830 6300
Fax: +1 703 830 2300
[email protected]
For editorial issues, like the status of your submitted paper or proposals, write to [email protected]
IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
Tel: +31 20 688 3355
Fax: +31 20 687 0091
[email protected]
For editorial issues, permissions, book requests, submissions and proceedings, contact the Amsterdam office [email protected]
Inspirees International (China Office)
Ciyunsi Beili 207(CapitaLand), Bld 1, 7-901
100025, Beijing
China
Free service line: 400 661 8717
Fax: +86 10 8446 7947
[email protected]
For editorial issues, like the status of your submitted paper or proposals, write to [email protected]
如果您在出版方面需要帮助或有任何建, 件至: [email protected]