Formal Languages and Automata Theory
The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently.…
Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose…
We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way…
Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…
In this article we introduce the operations of insertion and deletion working in a random-context and semi-conditional manner. We show that the conditional use of rules strictly increase the computational power. In the case of…
Linguistic variables represent crisp information in a form and precision appropriate for the problem. For example, to answer the question "How are you?" one may say "I am fine." the linguistic variables like "fine", so common in everyday…
Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to…
Finite state machines are widely used as a sound mathematical formalism that appropriately describes large scale, distributed and complex systems. Multiple interactions of finite state machines in complex systems are well captured by the…
The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is…
Operator precedence grammars define a classical Boolean and deterministic context-free family (called Floyd languages or FLs). FLs have been shown to strictly include the well-known visibly pushdown languages, and enjoy the same nice…
We revisit the problem of deciding whether a given string is uniquely decodable from its bigram counts by means of a finite automaton. An efficient algorithm for constructing a polynomial-size nondeterministic finite automaton that decides…
Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that…
In this paper we propose a biomolecular implementation of the push-down automaton (one of theoretical models of computing device with unbounded memory) using DNA molecules. The idea of this improved implementation was inspired by Cavaliere…
Hairpin completion and its variant called bounded hairpin completion are operations on formal languages, inspired by a hairpin formation in molecular biology. Another variant called hairpin lengthening has been recently introduced and…
The synchronization problem is investigated for the class of locally strongly transitive automata introduced in a previous work of the authors. Some extensions of this problem related to the notions of stable set and word of minimal rank of…
The automata arising from the well known conversion of regular expression to non deterministic automata have rather particular transition graphs. We refer to them as the Glushkov graphs, to honour his nice expression-to-automaton…
The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as…
Regular expressions provide a flexible means for matching strings and they are often used in data-intensive applications. They are formally equivalent to either deterministic finite automata (DFAs) or nondeterministic finite automata…
In this paper we consider a general way of constructing profinite struc- tures based on a given framework - a countable family of objects and a countable family of recognisers (e.g. formulas). The main theorem states: A subset of a family…
Answering a recent question of Crochemore, we prove that the language of words that are not abelian squares is not context-free.