Search results for "Formal language"
showing 10 items of 357 documents
Graph connectivity and monadic NP
2002
Ehrenfeucht games are a useful tool in proving that certain properties of finite structures are not expressible by formulas of a certain type. In this paper a new method is introduced that allows the extension of a local winning strategy for Duplicator, one of the two players in Ehrenfeucht games, to a global winning strategy. As an application it is shown that graph connectivity cannot be expressed by existential second-order formulas, where the second-order quantification is restricted to unary relations (monadic NP), even, in the presence of a built-in linear order. As a second application it is stated, that, on the other hand, the presence of a linear order increases the power of monadi…
On the regularity of circular splicing languages : A survey and new developments
2009
Circular splicing has been introduced to model a specific recombinant behaviour of circular DNA, continuing the investigation initiated with linear splicing. In this paper we focus on the relationship between regular circular languages and languages generated by finite circular splicing systems. We survey the known results towards a characterization of the intersection between these two classes and provide new contributions on the open problem of finding this characterization. First, we exhibit a non-regular circular language generated by a circular simple system thus disproving a known result in this area. Then we give new results related to a restrictive class of circular splicing systems…
On a Conjecture on Bidimensional Words
2003
We prove that, given a double sequence w over the alphabet A (i.e. a mapping from Z2 to A), if there exists a pair (n0, m0) ∈ Z2 such that pw(n0, m0) < 1/100n0m0, then w has a periodicity vector, where pw is the complexity function in rectangles of w.
Sturmian Graphs and a conjecture of Moser
2004
In this paper we define Sturmian graphs and we prove that all of them have a “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of CDAWGs of central Sturmian words. We show also that, analogously to the case of Sturmian words, these graphs converge to infinite ones.
On the Power of Tree-Walking Automata
2000
Tree-walking automata (TWAs) recently received new attention in the fields of formal languages and databases. Towards a better understanding of their expressiveness, we characterize them in terms of transitive closure logic formulas in normal form. It is conjectured by Engelfriet and Hoogeboom that TWAs cannot define all regular tree languages, or equivalently, all of monadic second-order logic. We prove this conjecture for a restricted, but powerful, class of TWAs. In particular, we show that 1-bounded TWAs, that is TWAs that are only allowed to traverse every edge of the input tree at most once in every direction, cannot define all regular languages. We then extend this result to a class …
Unary Languages Recognized by Two-Way One-Counter Automata
2014
A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages. Up to our knowledge, the only known unary nonregular languages recognized by 2D1CAs are those formed by strings having exponential length, where the exponents form some trivial unary regular language. In this paper, we present some non-trivial subsets of these languages. By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear–space Turing machines. We also show …
Regular Varieties of Automata and Coequations
2015
In this paper we use a duality result between equations and coequations for automata, proved by Ballester-Bolinches, Cosme-Ll´opez, and Rutten to characterize nonempty classes of deterministic automata that are closed under products, subautomata, homomorphic images, and sums. One characterization is as classes of automata defined by regular equations and the second one is as classes of automata satisfying sets of coequations called varieties of languages. We show how our results are related to Birkhoff’s theorem for regular varieties.
Deterministic generalized automata
1995
A generalized automaton (GA) is a finite automaton where the single transitions are defined on words rather than on single letters. Generalized automata were considered by K. Hashiguchi who proved that the problem of calculating the size of a minimal GA is decidable.
The Complexity of Probabilistic versus Quantum Finite Automata
2002
We present a language Ln which is recognizable by a probabilistic finite automaton (PFA) with probability 1 - ? for all ? > 0 with O(log2 n) states, with a deterministic finite automaton (DFA) with O(n) states, but a quantum finite automaton (QFA) needs at least 2?(n/log n) states.
Non-constructive Methods for Finite Probabilistic Automata
2007
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.