Search results for "Formal Language"
showing 10 items of 357 documents
GEOMETRIC EQUIVALENCE OF ALGEBRAS
2001
In this paper, we study the geometric equivalence of algebras in several varieties of algebras. We solve some of the problems formulated in [2], in particular, that of geometric equivalence for real-closed fields and finitely generated commutative groups.
Algebraic Results on Quantum Automata
2004
We use tools from the algebraic theory of automata to investigate the class of languages recognized by two models of Quantum Finite Automata (QFA): Brodsky and Pippenger’s end-decisive model, and a new QFA model whose definition is motivated by implementations of quantum computers using nucleo-magnetic resonance (NMR). In particular, we are interested in the new model since nucleo-magnetic resonance was used to construct the most powerful physical quantum machine to date. We give a complete characterization of the languages recognized by the new model and by Boolean combinations of the Brodsky-Pippenger model. Our results show a striking similarity in the class of languages recognized by th…
On Combinatorial Generation of Prefix Normal Words
2014
A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present an efficient algorithm for exhaustively listing the prefix normal words with a fixed length. The algorithm is based on the fact that the language of prefix normal words is a bubble language, a class of binary languages with the property that, for any word w in the language, exchanging the first occurrence of 01 by 10 in w results in another word in the language. We prove that each prefix normal word is produced in O(n) amortized time, and conjecture, based on expe…
A NEW COMPLEXITY FUNCTION FOR WORDS BASED ON PERIODICITY
2013
Motivated by the extension of the critical factorization theorem to infinite words, we study the (local) periodicity function, i.e. the function that, for any position in a word, gives the size of the shortest square centered in that position. We prove that this function characterizes any binary word up to exchange of letters. We then introduce a new complexity function for words (the periodicity complexity) that, for any position in the word, gives the average value of the periodicity function up to that position. The new complexity function is independent from the other commonly used complexity measures as, for instance, the factor complexity. Indeed, whereas any infinite word with bound…
Research of Complex Forms in Cellular Automata by Evolutionary Algorithms
2004
This paper presents an evolutionary approach for the search for new complex cellular automata. Two evolutionary algorithms are used: the first one discovers rules supporting gliders and periodic patterns, and the second one discovers glider guns in cellular automata. An automaton allowing us to simulate AND and NOT gates is discovered. The results are a step toward the general simulation of Boolean circuits by this automaton and show that the evolutionary approach is a promising technic for searching for cellular automata that support universal computation.
A New Universal Cellular Automaton Discovered by Evolutionary Algorithms
2004
In Twenty Problems in the Theory of Cellular Automata, Stephen Wolfram asks “how common computational universality and undecidability [are] in cellular automata.” This papers provides elements of answer, as it describes how another universal cellular automaton than the Game of Life (Life) was sought and found using evolutionary algorithms. This paper includes a demonstration that consists in showing that the presented R automaton can both implement any logic circuit (logic universality) and a simulation of Life (universality in the Turing sense).
On the lattice of prefix codes
2002
AbstractThe natural correspondence between prefix codes and trees is explored, generalizing the results obtained in Giammarresi et al. (Theoret. Comput. Sci. 205 (1998) 1459) for the lattice of finite trees under division and the lattice of finite maximal prefix codes. Joins and meets of prefix codes are studied in this light in connection with such concepts as finiteness, maximality and varieties of rational languages. Decidability results are obtained for several problems involving rational prefix codes, including the solution to the primeness problem.
On the decomposition of prefix codes
2017
Abstract In this paper we focus on the decomposition of rational and maximal prefix codes. We present an effective procedure that allows us to decide whether such a code is decomposable. In this case, the procedure also produces the factors of some of its decompositions. We also give partial results on the problem of deciding whether a rational maximal prefix code decomposes over a finite prefix code.
Burrows–Wheeler transform and Sturmian words
2003
Elements of Language Theory
1988
In this chapter we shall review the mathematical and computer science background on which the presentation in this book is based. We shall discuss the elements of discrete mathematics and formal language theory, emphasizing those issues that are of importance from the point of view of context-free parsing. We shall devote a considerable part of this chapter to matters such as random access machines and computational complexity. These will be relevant later when we derive efficient algorithms for parsing theoretic problems or prove lower bounds for the complexity of these problems. In this chapter we shall also discuss a general class of formal language descriptors called “rewriting systems”…