Title: Homomorphic images and shuffle product on probabilistic automata

Authors: J. Arockia Jeyakumar; T. Rajaretnam

Addresses: PG and Research Department of Mathematics, St. Joseph's College (Autonomous), Tiruchirappalli-620 002, Tamilnadu, India ' PG and Research Department of Mathematics, St. Joseph's College (Autonomous), Tiruchirappalli-620 002, Tamilnadu, India

Abstract: A probabilistic automaton (pa) is a fuzzy automaton, in which, sum of all fuzzy memberships of the initial states is one and from each state, on an input symbol, the sum of the fuzzy memberships of the transitions is one. In pa, it is shown that, if h : Γ^* → Σ^* is a morphism and h^–1 (λ) = λ, then the image of a recognisable subset of Γ^* is a recognisable subset of Σ^* and if h is fine, then the inverse image of recognisable subset of Σ^* is recognisable. It is also proved that the shuffle product of any two recognisable sets is recognisable.

Keywords: probabilistic automaton; probabilistic behaviour; fine morphism; shuffle product.

DOI: 10.1504/IJAISC.2019.105000

International Journal of Artificial Intelligence and Soft Computing, 2019 Vol.7 No.1, pp.3 - 12

Received: 23 Jan 2019
Accepted: 14 Apr 2019
Published online: 10 Feb 2020 *

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