Search results for "Formal Language"
showing 10 items of 357 documents
Pseudocomplements in sum-ordered partial semirings
2007
We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings – those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.
The expressive power of the shuffle product
2010
International audience; There is an increasing interest in the shuffle product on formal languages, mainly because it is a standard tool for modeling process algebras. It still remains a mysterious operation on regular languages.Antonio Restivo proposed as a challenge to characterize the smallest class of languages containing the singletons and closed under Boolean operations, product and shuffle. This problem is still widely open, but we present some partial results on it. We also study some other smaller classes, including the smallest class containing the languages composed of a single word of length 2 which is closed under Boolean operations and shuffle by a letter (resp. shuffle by a l…
On Horn spectra
1991
Abstract A Horn spectrum is a spectrum of a Horn sentence. We show that to solve Asser's problem, and consequently the EXPTIME = ? NEXPTIME question it suffices to consider the class of Horn spectra. We also pose the problem whether or not the generator of every Horn spectrum is a spectrum. We prove that from a negative solution of the generator problem, a negative answer for the EXPTIME = ? NEXPTIME question follows. Some other relations between the generator problem and Asser's problem are given. Finally, the relativized version of the generator problem is formulated and it is shown that it has an affirmative solution for some oracles, and a negative solution for some others.
Models of Computation, Riemann Hypothesis, and Classical Mathematics
1998
Classical mathematics is a source of ideas used by Computer Science since the very first days. Surprisingly, there is still much to be found. Computer scientists, especially, those in Theoretical Computer Science find inspiring ideas both in old notions and results, and in the 20th century mathematics. The latest decades have brought us evidence that computer people will soon study quantum physics and modern biology just to understand what computers are doing.
The dual equivalence of equations and coequations for automata
2015
The transition structure α : X ? X A of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. We use this algebra-coalgebra duality as a common perspective for the study of equations and coequations. For every automaton ( X , α ) , we define two new automata: free ( X , α ) and cofree ( X , α ) representing, respectively, the greatest set of equations and the smallest set of coequations satisfied by ( X , α ) . Both constructions are shown to be functorial. Our main result is that the restrictions of free and cofree to, respectively, preformations of languages and to quotients A * / C of A * with respect to a congr…
A Formalism Supplementing Cognitive Semantics Based on Mereology
2007
ABSTRACT This paper is motivated by and aims to supplement Cognitive Semantics. Details of this latter prominent approach within contemporary linguistic research will not be discussed here. Rather, we focus on a formalization of the concept of Gestalt and provide a formal semantics that can be used to interpret a certain formal language (LM 0) with respect to a universe of structured wholes (Gestalts). Since a great deal of the analyses of linguistic organization that has been provided by Cognitive Semantics since the mid-1970s is based on the concept of Gestalt, the semantics unfolded in the following may be viewed as an attempt to provide a starting point for supplementing the yet informa…
Languages with mismatches
2007
AbstractIn this paper we study some combinatorial properties of a class of languages that represent sets of words occurring in a text S up to some errors. More precisely, we consider sets of words that occur in a text S with k mismatches in any window of size r. The study of this class of languages mainly focuses both on a parameter, called repetition index, and on the set of the minimal forbidden words of the language of factors of S with errors. The repetition index of a string S is defined as the smallest integer such that all strings of this length occur at most in a unique position of the text S up to errors. We prove that there is a strong relation between the repetition index of S an…
Balance Properties and Distribution of Squares in Circular Words
2008
We study balance properties of circular words over alphabets of size greater than two. We give some new characterizations of balanced words connected to the Kawasaki-Ising model and to the notion of derivative of a word. Moreover we consider two different generalizations of the notion of balance, and we find some relations between them. Some of our results can be generalised to non periodic infinite words as well.
Hamming, Permutations and Automata
2007
Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A.Ambainis and R.Freivalds that quantum finite automata with pure states can have exponentially smaller number of states than deterministic finite automata recognizing the same language. There was a never published "folk theorem" proving that quantum finite automata with mixed states are no more than superexponentially more concise than deterministic finite automata. It was not known whether the super-exponential advantage of quantum automata is really achievable. We prove that there is an infinite sequence of distinct int…
Super-Exponential Size Advantage of Quantum Finite Automata with Mixed States
2008
Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A.Ambainis and R.Freivalds that quantum finite automata with pure states can have exponentially smaller number of states than deterministic finite automata recognizing the same language. There was a never published "folk theorem" proving that quantum finite automata with mixed states are no more than super-exponentially more concise than deterministic finite automata. It was not known whether the super-exponential advantage of quantum automata is really achievable. We use a novel proof technique based on Kolmogorov complex…