All posts under category "Computer Science / Formal Languages"
For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called 'proper'. It is known that the Boolean semiring, the semiring of natural numbers, the ring of integers, all finite
Using combinatorial properties of incomplete sets in a free monoid we construct a series of n-state deterministic automata with zero whose shortest synchronizing word has length n^2/4+n/2-1.
Asynchronous programming is a ubiquitous systems programming idiom to manage concurrent interactions with the environment. In this style, instead of waiting for time-consuming operations to complete, the programmer makes a non-blocking call to the operation and posts a callback task to a task buffer
The combined trace (i.e., comtrace) notion was introduced by Janicki and Koutny in 1995 as a generalization of the Mazurkiewicz trace notion. Comtraces are congruence classes of step sequences, where the congruence relation is defined from two relations simultaneity and serializability on events. Th
Timed automata and register automata are well-known models of computation over timed and data words respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two mo
Answering a recent question of Crochemore, we prove that the language of words that are not abelian squares is not context-free.
We show that the problem of whether the fixed point of a morphism avoids Abelian $k$-powers is decidable under rather general conditions
In a previous paper, we described the set of words that appear in the coding of smooth (resp. analytic) curves at arbitrary small scale. The aim of this paper is to compute the complexity of those languages.
In this note, we give a construction that provides a tight lower bound of mn-1 for the length of the shortest word in the intersection of two regular languages with state complexities m and n.
We extend Carpi's results by showing that Dejean's conjecture holds for n >= 30.
Let S be a finite set of words over an alphabet Sigma. The set S is said to be complete if every word w over the alphabet Sigma is a factor of some element of S*, i.e. w belongs to Fact(S*). Otherwise if S is not complete, we are interested in finding bounds on the minimal length of words in Sigma*
Ligands for only two human olfactory receptors are known. One of them, OR1D2, binds to Bourgeonal [Malnic B, Godfrey P-A, Buck L-B (2004) The human olfactory receptor gene family. Proc. Natl. Acad. Sci U. S. A. 101: 2584-2589 and Erratum in: Proc Natl Acad Sci U. S. A. (2004) 101: 7205]. OR1D2, OR1D
In this paper, we construct a new weakly universal cellular automaton on the ternary heptagrid. The previous result, obtained by the same author and Y. Song required six states only. This time, the number of states is four. This is the best result up to date for cellular automata in the hyperbolic p
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with respect to Turing and circuit universality, we discuss construct
A language L is closed if L = L*. We consider an operation on closed languages, L-*, that is an inverse to Kleene closure. It is known that if L is closed and regular, then L-* is also regular. We show that the analogous result fails to hold for the context-free languages. Along the way we find a ne
The recently confirmed Dejean's conjecture about the threshold between avoidable and unavoidable powers of words gave rise to interesting and challenging problems on the structure and growth of threshold words. Over any finite alphabet with k >= 5 letters, Pansiot words avoiding 3-repetitions form a
In this paper, we have compared r.e. sets based on their enumeration orders with Turing machines. Accordingly, we have defined novel concept uniformity for Turing machines and r.e. sets and have studied some relationships between uniformity and both one-reducibility and Turing reducibility. Furtherm
The aim of this paper is to build a new family of lattices related to some combinatorial extremal sum problems, in particular to a conjecture of Manickam, Mikl'os and Singhi. We study the fundamentals properties of such lattices and of a particular class of boolean functions defined on them.
In this paper, we review some recent results about the use of dynamic observers for fault diagnosis of discrete event systems. Fault diagnosis consists in synthesizing a diagnoser that observes a given plant and identifies faults in the plant as soon as possible after their occurrence. Existing lite
This paper presents a novel technique for state space reduction of probabilistic specifications, based on a newly developed notion of confluence for probabilistic automata. We prove that this reduction preserves branching probabilistic bisimulation and can be applied on-the-fly. To support the techn
We settle the equivalence between the problem of hitting a polyhedral set by the orbit of a linear map and the intersection of a regular language and a language of permutations of binary words (the permutation filter realizability problem). The decidability of the both problems is presently unknown
We present probabilistic arithmetic automata (PAAs), a general model to describe chains of operations whose operands depend on chance, along with two different algorithms to exactly calculate the distribution of the results obtained by such probabilistic calculations. PAAs provide a unifying framewo
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 speech. In this paper an alternative interpretation of linguis
The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.
This volume represents the proceedings of the 5th Workshop on Membrane Computing and Biologically Inspired Process Calculi (MeCBIC 2011), held together with the 12th International Conference on Membrane Computing on 23rd August 2011 in Fontainebleau, France.
Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different spatial and temporal scales. Although several ways to provid
In this talk we are concerned with the intrinsic similarities and differences between Petri nets on the one hand, and membrane systems and reaction systems on the other hand.
The (-beta)-integers are natural generalisations of the beta-integers, and thus of the integers, for negative real bases. They can be described by infinite words which are fixed points of anti-morphisms. We show that they are not necessarily uniformly discrete and relatively dense in the real number
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 of recognisable sets is a lattice if and only if it is defi
In this paper we prove the decidability of the HD0L ultimate periodicity problem.
A filtration of a formal language L by a sequence s maps L to the set of words formed by taking the letters of words of L indexed only by s. We consider the languages resulting from filtering by all arithmetic progressions. If L is regular, it is easy to see that only finitely many distinct language
We construct an example of proof within the main formal system from arXiv:1010.4760v3, which is intended to capture the bisimulation equivalence for non-deterministic first-order grammars, and show that its conclusion is semantically false. We then locate and analyze the flawed argument in the sound
Reversing a (forward) computation history means undoing the history. In concurrent systems, undoing the history is not performed in a deterministic way but in a causally consistent fashion, where states that are reached during a backward computation are states that could have been reached during the
In this note, we present an infinite family of promise problems which can be solved exactly by just tuning transition amplitudes of a two-state quantum finite automata operating in realtime mode, whereas the size of the corresponding classical automata grow without bound.
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 unique decodability is given. Conversely, we show that the m
In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of parameters in a standard way. The free right algebra F(L, C) o
In this paper, we introduce the new concept of state complexity approximation, which is a further development of state complexity estimation. We show that this new concept is useful in both of the following two cases: the exact state complexities are not known and the state complexities have been ob
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