442 research outputs found
Turing machines based on unsharp quantum logic
In this paper, we consider Turing machines based on unsharp quantum logic.
For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce
E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic
Turing machines (EDTMs). We discuss different E-valued recursively enumerable
languages from width-first and depth-first recognition. We find that
width-first recognition is equal to or less than depth-first recognition in
general. The equivalence requires an underlying E value lattice to degenerate
into an MV algebra. We also study variants of ENTMs. ENTMs with a classical
initial state and ENTMs with a classical final state have the same power as
ENTMs with quantum initial and final states. In particular, the latter can be
simulated by ENTMs with classical transitions under a certain condition. Using
these findings, we prove that ENTMs are not equivalent to EDTMs and that ENTMs
are more powerful than EDTMs. This is a notable difference from the classical
Turing machines.Comment: In Proceedings QPL 2011, arXiv:1210.029
On Intuitionistic Fuzzy Context-Free Languages
Taking intuitionistic fuzzy sets as the structures of truth values, we propose the notions of intuitionistic fuzzy context-free grammars (IFCFGs, for short) and pushdown automata with final states (IFPDAs). Then we investigate algebraic characterization of intuitionistic fuzzy recognizable languages including decomposition form and representation theorem. By introducing the generalized subset construction method, we show that IFPDAs are equivalent to their simple form, called intuitionistic fuzzy simple pushdown automata (IF-SPDAs), and then prove that intuitionistic fuzzy recognizable step functions are the same as those accepted by IFPDAs. It follows that intuitionistic fuzzy pushdown automata with empty stack and IFPDAs are equivalent by classical
automata theory. Additionally, we introduce the concepts of Chomsky normal form grammar (IFCNF) and Greibach normal form grammar (IFGNF) based on intuitionistic fuzzy sets. The results of our study indicate that intuitionistic fuzzy context-free languages generated by IFCFGs are equivalent to those generated by IFGNFs and IFCNFs, respectively, and they are also equivalent to intuitionistic fuzzy recognizable step functions. Then some operations on the family of intuitionistic fuzzy context-free languages are discussed. Finally, pumping lemma for intuitionistic fuzzy context-free languages is investigated
Fuzzy Automata: A Quantitative Review
Classical automata theory cannot deal with the system uncertainty. To deal with the system uncertainty the concept of fuzzy finite automata was proposed. Fuzzy automata can be used in diverse applications such as fault detection, pattern matching, measuring the fuzziness between strings, description of natural languages, neural network, lexical analysis, image processing, scheduling problem and many more. In this paper, a methodical literature review is carried out on various research works in the field of Fuzzy automata and explained the challenging issues in the field of fuzzy automata
A Bibliography on Fuzzy Automata, Grammars and Lanuages
This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing
A probabilistic model of computing with words
AbstractComputing 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
Weighted Logics for Nested Words and Algebraic Formal Power Series
Nested words, a model for recursive programs proposed by Alur and Madhusudan,
have recently gained much interest. In this paper we introduce quantitative
extensions and study nested word series which assign to nested words elements
of a semiring. We show that regular nested word series coincide with series
definable in weighted logics as introduced by Droste and Gastin. For this we
establish a connection between nested words and the free bisemigroup. Applying
our result, we obtain characterizations of algebraic formal power series in
terms of weighted logics. This generalizes results of Lautemann, Schwentick and
Therien on context-free languages
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