Probabilistic automata for computing with words

  • Authors:

  • Yongzhi Cao;Lirong Xia;Mingsheng Ying

  • Affiliations:

  • Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China and Key Laboratory of High Confidence Software Technologies, Ministry of Edu ...;SEAS, Harvard University, Cambridge, MA 02138, USA;Center for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, Australia and State Key Laboratory of Intelligent Techn ...

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2013

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Abstract

Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars for computing with (some special) words, where the words are interpreted as probabilistic distributions or possibility distributions over a set of crisp symbols. By probabilistic conditioning, we then establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling arbitrary inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with some special words. To compare the transition probabilities of two near inputs, we also examine some analytical properties of the transition probability functions of generalized extensions. Moreover, the retractions and the generalized extensions are shown to be equivalence-preserving. Finally, we clarify some relationships among the retractions, the generalized extensions, and the extensions studied by Qiu and Wang.