Fuzzy logic, neural networks, and soft computing
Communications of the ACM
Randomized algorithms
SIAM Journal on Computing
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Probabilistic Languages: A Review and Some Open Questions
ACM Computing Surveys (CSUR)
Quantum automata and quantum grammars
Theoretical Computer Science
Dense quantum coding and quantum finite automata
Journal of the ACM (JACM)
Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on Computing
1-way quantum finite automata: strengths, weaknesses and generalizations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Applying Probability Measures to Abstract Languages
IEEE Transactions on Computers
Determination of Probabilistic Grammars for Functionally Specified Probability-Measure Languages
IEEE Transactions on Computers
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy Systems
A formal model of computing with words
IEEE Transactions on Fuzzy Systems
Computing with words via Turing machines: a formal approach
IEEE Transactions on Fuzzy Systems
Ontological approach to development of computing with words based systems
International Journal of Approximate Reasoning
Automata theory based on complete residuated lattice-valued logic: Pushdown automata
Fuzzy Sets and Systems
Grammar theory based on lattice-ordered monoid
Fuzzy Sets and Systems
Approximation of fuzzy context-free grammars
Information Sciences: an International Journal
Lattice-valued fuzzy Turing machines: Computing power, universality and efficiency
Fuzzy Sets and Systems
A fuzzy Petri-nets model for computing with words
IEEE Transactions on Fuzzy Systems - Special section on computing with words
Automata theory based on complete residuated lattice-valued logic: Turing machines
Fuzzy Sets and Systems
Probabilistic automata for computing with words
Journal of Computer and System Sciences
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Computing in the traditional sense involves inputs with strings of numbers and symbols rather than words, where words mean probability distributions over input alphabet, and are different from the words in classical formal languages and automata theory. In this paper our goal is to deal with probabilistic finite automata (PFAs), probabilistic Turing machines (PTMs), and probabilistic context-free grammars (PCFGs) by inputting strings of words (probability distributions). Specifically, (i) we verify that PFAs computing strings of words can be implemented by means of calculating strings of symbols (Theorem 1); (ii) we elaborate on PTMs with input strings of words, and particularly demonstrate by describing Example 2 that PTMs computing strings of words may not be directly performed through only computing strings of symbols, i.e., Theorem 1 may not hold for PTMs; (iii) we study PCFGs and thus PRGs with input strings of words, and prove that Theorem 1 does hold for PCFRs and PRGs (Theorem 2); a characterization of PRGs in terms of PFAs, and the equivalence between PCFGs and their Chomsky and Greibach normal forms, in the sense that the inputs are strings of words, are also presented. Finally, the main results obtained are summarized, and a number of related issues for further study are raised.