The decidability of the equivalence problem for DOL-systems

The language and sequence equivalence problem for DOL-systems is shown to be decidable. In an algebraic formulation the sequence equivalence problem for DOL-systems can be stated as follows: Given homomorphisms h1 and h2 on a free monoid Σ* and a word σ from Σ*, is h1n(σ) = h2n(σ) for all n ⩾ 0

On a generalization of Abelian equivalence and complexity of infinite words

In this paper we introduce and study a family of complexity functions of infinite words indexed by k in Z^+ U {+infinity}. Let k in Z^+ U {+infinity} and A be a finite non-empty set. Two finite words u and v in A* are said to be k-Abelian equivalent if for all x in A* of length less than or equal to k, the number of occurrences of x in u is equal to the number of occurrences of x in v. This defines a family of equivalence relations sim_k on A*, bridging the gap between the usual notion of Abelian equivalence (when k = 1) and equality (when k = +infinity). We show that the number of k-Abelian equivalence classes of words of length n grows polynomially, although the degree is exponential in k. Given an infinite word omega in A^N, we consider the associated complexity function P^(k)_omega : N -> N which counts the number of k-Abelian equivalence classes of factors of omega of length n. We show that the complexity function P_k is intimately linked with periodicity. More precisely we define an auxiliary function q^k : N -> N and show that if P^(k)_omega(n) < q^k(n) for some k in Z^+ U {+infinity} and n >= 0, then omega is ultimately periodic. Moreover if omega is aperiodic, then P^(k)_omega(n) = q^k(n) if and only if omega is Sturmian. We also study k-Abelian complexity in connection with repetitions in words. Using Szemeredi's theorem, we show that if omega has bounded k-Abelian complexity, then for every D subset of N with positive upper density and for every positive integer N, there exists a k-Abelian N-power occurring in omega at some position j in D

Strategic logics : complexity, completeness and expressivity

by transferring normative attributes from an agent to another. Such interactions are called delegation. Formal models of delegation and control were studied in, e.g., [189, 149, 191]. In this work, we consider the scenario where agents delegate control over propositions to other agents. The distinction between controllable and uncontrollable propositions stems from areas like discrete event systems and control theory, where, e.g., Boutilier [39] studied control in the context of deontic logic. Control and controllable propositions were also studied in [52, 66, 249, 248]. We now give an overview of the thesis. The main purpose of Chapter 2 is to introduce basic concepts and notation and to review relevant literature. The first section presents a brief survey on modal logic. Then, in sections 2.2, 2.3 and 2.4, we introduce epistemic, temporal and strategic modal logics and state known results that characterise their expressivity and computational complexity. In particular, we consider variants of ATL as extensions of branching-time logics. With such ATL-like logics we can describe dynamic multi-agent interactions. In Section 2.5, we discuss extensions of ATL with epistemic notions. Additionally, we suggest a framework for memory-bounded strategic reasoning. In particular, we introduce an epistemic variant of ATL that accounts for agents with limited memory resources as this case was neglected in the literature to date. In Chapter 3, we investigate the computational complexity of ATL and its epistemic extension ATEL. We show in detail how 'the complexity of the satisfiability problem for both logics can be settled at ExpTIME-complete. The part of the chapter about ATL is based on the paper 'ATL Satisfiability is Indeed ExpTIME-COmplete' by Walther, Lutz, Wolter and Wooldridge in the Journal of Logic and Computation, 2006 (265)' and the part about ATEL is based on the paper 'ATEL with Common and Distributed Knowledge is ExpTime-Complete' by Walther which was presented at the 4th Workshop on Methods for Modalities, Humbolt University, Berlin, December 1-2, 2005 [264]. In Chapter 4, we aim to extend the expressiveness of ATL without increasing its computational complexity. We introduce explicit names for strategies in the object language and extend modal operators with the possibility to bind agents to strategy names. In this way, we can fix the decisions of agents that possibly belong to several coalitions. By identifying the behaviqur of agents, we can reason about the effects of agents changing coalitions. Dynamic coalitions provide more flexibility to adapt abilities to a changing environment. We investigate the expressivity of the resulting logic ATLES and compare it to ATL and ATL*. Moreover, we formulate two model checking problems for ATLES and investigate their complexity as well as the complexity of the satisfiability problem for ATLES. Additionally, we present a complete axiomatisation. This chapter is based on the paper 'Alternating-time Temporal Logic with Explicit Strategies' by Walther, van der Hoek and Wooldridge which is going to presented at the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK), Brussels, Belgium, June 25-27, 2007 [266]

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration

The field of analytic combinatorics, which studies the asymptotic behaviour of sequences through analytic properties of their generating functions, has led to the development of deep and powerful tools with applications across mathematics and the natural sciences. In addition to the now classical univariate theory, recent work in the study of analytic combinatorics in several variables (ACSV) has shown how to derive asymptotics for the coefficients of certain D-finite functions represented by diagonals of multivariate rational functions. We give a pedagogical introduction to the methods of ACSV from a computer algebra viewpoint, developing rigorous algorithms and giving the first complexity results in this area under conditions which are broadly satisfied. Furthermore, we give several new applications of ACSV to the enumeration of lattice walks restricted to certain regions. In addition to proving several open conjectures on the asymptotics of such walks, a detailed study of lattice walk models with weighted steps is undertaken.Comment: PhD thesis, University of Waterloo and ENS Lyon - 259 page

Ordonnancement hybride des applications flots de données sur des systèmes embarqués multi-coeurs

Les systèmes embarqués sont de plus en plus présents dans l'industrie comme dans la vie quotidienne. Une grande partie de ces systèmes comprend des applications effectuant du traitement intensif des données: elles utilisent de nombreux filtres numériques, où les opérations sur les données sont répétitives et ont un contrôle limité. Les graphes "flots de données", grâce à leur déterminisme fonctionnel inhérent, sont très répandus pour modéliser les systèmes embarqués connus sous le nom de "data-driven". L'ordonnancement statique et périodique des graphes flot de données a été largement étudié, surtout pour deux modèles particuliers: SDF et CSDF. Dans cette thèse, on s'intéresse plus particulièrement à l'ordonnancement périodique des graphes CSDF. Le problème consiste à identifier des séquences périodiques infinies d'actionnement des acteurs qui aboutissent à des exécutions complètes à buffers bornés. L'objectif est de pouvoir aborder ce problème sous des angles différents : maximisation de débit, minimisation de la latence et minimisation de la capacité des buffers. La plupart des travaux existants proposent des solutions pour l'optimisation du débit et négligent le problème d'optimisation de la latence et propose même dans certains cas des ordonnancements qui ont un impact négatif sur elle afin de conserver les propriétés de périodicité. On propose dans cette thèse un ordonnancement hybride, nommé Self-Timed Périodique (STP), qui peut conserver les propriétés d'un ordonnancement périodique et à la fois améliorer considérablement sa performance en terme de latence.One of the most important aspects of parallel computing is its close relation to the underlying hardware and programming models. In this PhD thesis, we take dataflow as the basic model of computation, as it fits the streaming application domain. Cyclo-Static Dataflow (CSDF) is particularly interesting because this variant is one of the most expressive dataflow models while still being analyzable at design time. Describing the system at higher levels of abstraction is not sufficient, e.g. dataflow have no direct means to optimize communication channels generally based on shared buffers. Therefore, we need to link the dataflow MoCs used for performance analysis of the programs, the real time task models used for timing analysis and the low-level model used to derive communication times. This thesis proposes a design flow that meets these challenges, while enabling features such as temporal isolation and taking into account other challenges such as predictability and ease of validation. To this end, we propose a new scheduling policy noted Self-Timed Periodic (STP), which is an execution model combining Self-Timed Scheduling (STS) with periodic scheduling. In STP scheduling, actors are no longer strictly periodic but self-timed assigned to periodic levels: the period of each actor under periodic scheduling is replaced by its worst-case execution time. Then, STP retains some of the performance and flexibility of self-timed schedule, in which execution times of actors need only be estimates, and at the same time makes use of the fact that with a periodic schedule we can derive a tight estimation of the required performance metrics