The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
While a mature theory around logics such as MSO, LTL, and CTL has been developed in the pure boolean setting of finite automata, weighted automata lack such a natural connection with (temporal) logic and related verification algorithms. In this paper, we will identify weighted versions of MSO and CTL that generalize the classical logics and even other quantitative extensions such as probabilistic...
This is a survey on some undecidable problems on integer matrices. The proofs of these results employ special instances, called Claus instances, of the Post Correspondence Problem. The presentation is based on the article Halava et al. “Undecidability bounds for integer matrices using Claus instances” (Internat. J. Foundations of Comput. Sci. 18, 2007, 931–948).
This is a talk on the size complexity of two-way finite automata. We present the central open problem in the area, explain a motivation behind it, recall its early history, and introduce some of the concepts used in its study. We then sketch a possible future, describe a natural systematic way of pursuing it, and record some of the progress that has been achieved. We add little to what is already...
In this paper, we establish the Černý-Pin conjecture for automata with the property that their transition monoid cannot recognize the language {a,b}*ab{a,b}*. For the subclass of automata whose transition monoids have the property that each regular -class is a subsemigroup, we give a tight bound on lengths of reset words for synchronizing automata thereby answering a question of Volkov.
Černý’s conjecture asserts the existence of a synchronizing word of length at most (n − 1)2 for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p,q, one has p ·a...
In this paper we consider the class of all regular languages definable by the extended majority quantifier and the order predicate but using only two variables. The main part of the paper is the presentation of a geometric method which is used to show that a given regular language cannot be defined by such formulas. Applying this method we can give a necessary condition in terms of an equation as...
We study the problem of testing whether a context-free language is included in a fixed set L0, where L0 is the language of words reducing to the empty word in the monoid defined by a complete string rewrite system. We prove that, if the monoid is cancellative, then our inclusion problem is polynomially reducible to the problem of testing equivalence of straight-line programs...
Blanchet-Sadri et al. have shown that Avoidability, or the problem of deciding the avoidability of a finite set of partial words over an alphabet of size k ≥ 2, is -hard [Theoret. Comput. Sci. 410 (2009) 968–972]. Building on their work, we analyze in this paper the complexity of natural variations on the problem. While some of them are -hard, others are shown...
A famous theorem of Kuratowski states that, in a topological space, at most 14 distinct sets can be produced by repeatedly applying the operations of closure and complement to a given set. We re-examine this theorem in the setting of formal languages, where closure is either Kleene closure or positive closure. We classify languages according to the structure of the algebra they generate under iterations...
In this paper we investigate the periodic structure of rich words (i.e., words having the highest possible number of palindromic factors), giving new results relating them with periodic-like words. In particular, some new characterizations of rich words and rich palindromes are given. We also prove that a periodic-like word is rich if and only if the square of its fractional root is also rich.
This is a new applied development of trace theory to compilation. Trace theory allows to commute independent program instructions, but overlooks the differences between control and data dependencies. Control(C)-dependences, unlike data-dependences, are determined by the Control Flow Graph, modelled as a local DFA. To ensure semantic equivalence, partial commutation must preserve C-dependences. New...
In this paper, we study rational relations that are both left and right synchronous. We show that these relations are boolean combinations of almost length preserving relations, length comparing relations and recognizable relations.
One of the particularities of information encoded as DNA strands is that a string u contains basically the same information as its Watson-Crick complement, denoted here as θ(u). Thus, any expression consisting of repetitions of u and θ(u) can be considered in some sense periodic. In this paper we give a generalization of Lyndon and Schützenberger’s classical result about equations of the form u ...
We show here how to construct a cellular automaton whose asymptotic set (the set of configurations it converges to) is maximally complex: it contains only configurations of maximal Kolmogorov complexity. This cellular automaton hence exhibits the most complex possible asymptotic behavior.
We consider algorithms for approximating context–free grammars by regular grammars, making use of Chomsky’s characterization of non–self–embedding grammars as generating regular languages and a transformation by Mohri and Nederhof on sets of mutually recursive nonterminals. We give an exposition of strongly regular grammars and this transformation, and use it as a subprocedure to obtain tighter regular...
In this paper we prove that it is decidable whether the set pow(L), which we get by taking all the powers of all the words in some regular language L, is regular or not. The problem was originally posed by Calbrix and Nivat in 1995. Partial solutions have been given by Cachat for unary languages and by Horváth et al. for various kinds of exponent sets for the powers and regular languages which have...
In the present paper, we study the existence of descriptive patterns, i. e. patterns that cover all words in a given set through morphisms and that are optimal in terms of revealing commonalities of these words. Our main result shows that if patterns may be mapped onto words by arbitrary morphisms, then there exist infinite sets of words that do not have a descriptive pattern. This answers a question...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.