We investigate well-structured graph-driven parity-FBDDs, which strictly generalize the two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Boolean functions represented by well-structured graph-driven parity-FBDDs in terms of invariants of the function represented and the graph-ordering used. As a consequence, we derive a lower bound criterion and prove an exponential lower bound for certain linear code functions. The second main result of this paper is a polynomial time algorithm that minimizes the number of nodes in a graph-driven parity-FBDD.

We prove that, with high probability, the space complexity of refuting a random unsatisfiable Boolean formula in k-CNF on n variables and m = Δn clauses is $O\left(n \cdot \Delta^{-\frac{1}{k-2}}\right)$.

We prove a long standing conjecture of Duval in the special case of Sturmian words.

Given an ordered alphabet and a permutation, according to the lexicographic order, on the set of suffixes of a word w, we present in this article a linear time and space method to determine whether a word w' has the same permutation on its suffixes. Using this method, we are then also able to build the class of all the words having the same permutation on their suffixes, first of all the smallest one. Finally, we note that this work can lead to a method for generating a Lyndon word randomly in linear time or for computing the set of Lyndon words of length n .

We study the decidability of the following problem: given p affine functions ƒ1,...,ƒp over $\mathbb{N}^k$ and two vectors $v_1, v_2\in\mathbb{N}^k$, is v2 reachable from v1 by successive iterations of ƒ1,...,ƒp (in this given order)? We show that this question is decidable for p = 1, 2 and undecidable for some fixed p.

We show that the validity of Parikh's theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of μ-term equations of continuous commutative idempotent semirings.

Word and tree codes are studied in a common framework, that of polypodes which are sets endowed with a substitution like operation. Many examples are given and basic properties are examined. The code decomposition theorem is valid in this general setup.

We show that some natural refinements of the Straubing and Brzozowskihierarchies correspond (via the so called leaf-languages) step by step tosimilar refinements of the polynomial-time hierarchy. This extends a result of Burtschik and Vollmer on relationship between the Straubing and thepolynomial hierarchies. In particular, this applies to the Boolean hierarchyand the plus-hierarchy.


A shuffle ideal is a language which is a finite union of languages of the form A*a1A*...A*ak where A is a finite alphabet and the ai's are letters. We show how to represent shuffle ideals by special automata and how to compute these representations. We also give a temporal logic characterization of shuffle ideals and we study its expressive power over infinite words. We characterize the complexity of deciding whether a language is a shuffle ideal and we give a new quadratic algorithm for this problem. Finally we also present a characterization by subwords of the minimal automaton of a shuffle ideal and study the complexity of basic operations on shuffle ideals.

It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem of finding the set of winning positions in a parity game. The algorithm can be seen as a reduction of a parity to a safety game and computation of the set of winning positions in the resulting game.

Monads have been employed in programming languages for modeling various language features, most importantly those that involve side effects. In particular, Haskell's IO monad provides access to I/O operations and mutable variables, without compromising referential transparency. Cyclic definitions that involve monadic computations give rise to the concept of value-recursion, where the fixed-point computation takes place only over the values, without repeating or losing effects. In this paper, we describe a semantics for a lazy language based on Haskell, supporting monadic I/O, mutable variables, usual recursive definitions, and value recursion. Our semantics is composed of two layers: a natural semantics for the functional layer, and a labeled transition semantics for the IO layer.

We show that, for any stochastic event p of period n, there exists a measure-once one-way quantum finite automaton (1qfa) with at most $2\sqrt{6n}+25$ states inducing the event ap+b, for constants a>0, b ≥ 0, satisfying a+b ≥ 1. This fact is proved by designing an algorithm which constructs the desired 1qfa in polynomial time. As a consequence, we get that any periodic language of period n can be accepted with isolated cut point by a 1qfa with no more than $2\sqrt{6n}+26$ states. Our results give added evidence of the strength of measure-once 1qfa's with respect to classical automata.

The class of weak parallel machines is interesting, because it contains somerealistic parallel machine models, especially suitable for pipelinedcomputations. We prove that a modification of the bulk synchronous parallel(BSP) machine model, called decomposable BSP (dBSP), belongs to the class ofweak parallel machines if restricted properly. We will also correct someearlier results about pipelined parallel Turing machines.

Here we give a characterization of Arnoux–Rauzy sequences by the way of the lexicographic orderings of their alphabet.

We introduce a notion of category with feedback-with-delay, closely related to the notion of traced monoidal category, and show that the Circ construction of [15] is the free category with feedback on a symmetric monoidal category. Combining with the Int construction of Joyal et al. [12] we obtain a description of the free compact closed category on a symmetric monoidal category. We thus obtain a categorical analogue of the classical localization of a ring with respect to a multiplicative subset. In this context we define a notion of fixed-point semantics of a category with feedback which is seen to include a variety of classical semantics in computer science.

Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.

In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.

For any finite word w on a finite alphabet, we consider the basic parameters Rw and Kw of w defined as follows: Rw is the minimal natural number for which w has no right special factor of length Rw and Kw is the minimal natural number for which w has no repeated suffix of length Kw. In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.

For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by μ-terms. We call the category μ-bicomplete if every μ-term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved through parity games: we associate to each game an algebraic expression and turn the game into a term of a categorical theory. We show that μ-terms and parity games are equivalent, meaning that they define the same property of being μ-bicomplete. Finally, the interpretation of a parity game in the category of sets is shown to be the set of deterministic winning strategies for a chosen player.