We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the learning type InfEx≅, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is InfEx≅-learnable if and only if the structures can be distinguished in

We define and explore a notion of unique prime factorization for constraint functions, and use this as a new tool to prove a complexity classification for counting weighted Eulerian orientation problems with arrow reversal symmetry (ars). We prove that all such problems are either polynomial-time computable or #P-hard. We show that the class of weighted Eulerian orientation problems subsumes all weighted

A multi-stack pushdown system is a natural model of concurrent programs. The basic verification problems are in general undecidable (two stacks suffice to encode a Turing machine), and in the last years, there have been some successful approaches based on under-approximating the system behaviors. In this paper, we propose a restriction of the semantics of the general model such that a symbol that is

We present the link-calculus, an extension of π-calculus, that models interactions that are multiparty, i.e. that may involve more than two processes, mutually exchanging data. Communications are seen as chains of suitably combined links (which record the source and the target ends of each hop of interactions), each contributed by one party. Values are exchanged by means of message tuples, still provided

The PQ-tree is a fundamental data structure that has also been used in comparative genomics to model ancestral genomes with some uncertainty. To quantify the evolution between genomes represented by PQ-trees, in this paper we study two fundamental problems of PQ-tree comparison motivated by this application. First, we show that the problem of comparing two PQ-trees by computing the minimum breakpoint

Well-structured transition systems form a large class of infinite-state systems, for which safety verification is decidable thanks to a generic backward coverability algorithm. However, for several classes of systems, the generic upper bounds one can extract from the algorithm are far from optimal. In particular, in the case of vector addition systems (VAS) and several of their extensions, the known

Interrupt Timed Automata (ITA ) form a subclass of stopwatch automata where reachability and some variants of timed model checking are decidable even in presence of parameters. They are well suited to model and analyze real-time operating systems. Here we extend ITA with polynomial guards and updates, leading to the class of polynomial ITA (PolITA ). We prove that reachability is decidable in 2EXPTIME

This work studies which storage mechanisms in automata permit decidability of the emptiness problem. The question is formalized using valence automata, an abstract model of automata in which the storage mechanism is given by a monoid. For each of a variety of storage mechanisms, one can choose a (typically infinite) monoid M such that valence automata over M are equivalent to (one-way) automata with

A usual way to find positive invariant sets of ordinary differential equations is to restrict the search to predefined finitely generated shapes, such as linear templates, or ellipsoids as in classical quadratic Lyapunov function based approaches. One then looks for generators or parameters for which the corresponding shape has the property that the flow of the ODE goes inwards on its border. But for

We propose a notion of alternating bisimulation for strategic abilities under imperfect information. The bisimulation preserves formulas of ATL⁎ for both the objective and subjective variants of the state-based semantics with imperfect information, which are commonly used in the modeling and verification of multi-agent systems. Furthermore, we apply the theoretical result to the verification of coercion-resistance

We study multi-player turn-based games played on (potentially infinite) directed graphs. An outcome is assigned to every play of the game. Each player has a preference relation on the set of outcomes which allows him to compare plays. We focus on the recently introduced notion of weak subgame perfect equilibrium (weak SPE). This is a variant of the classical notion of SPE, where players who deviate

We develop a game-theoretic semantics (GTS) for the fragment ATL+ of the alternating-time temporal logic ATL⁎, thereby extending the recently introduced GTS for ATL. We show that the game-theoretic semantics is equivalent to the standard compositional semantics of ATL+ with perfect-recall strategies. Based on the new semantics, we provide an analysis of the memory and time resources needed for model

Linear Dynamic Logic on finite traces (LDLF) is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLF. This study builds upon a generalisation of Boolean games, a logic-based game model

This paper studies the computation of mixed Nash equilibria in weighted Boolean games. In weighted Boolean games, players aim to maximise the total expected weight of a set of formulas by selecting behavioural strategies, that is, randomisations over the truth assignments for each propositional variable under their unique control. Behavioural strategies thus present a compact representation of mixed

We investigate the existence of various types of equilibria (Nash, subgame perfect, Pareto-optimal, secure) in multi-player multi-outcome infinite sequential games. Our results are transfer theorems: Assuming determinacy for a class of simple two-player win/lose games, we obtain existence results about equilibria in the associated multi-player multi-outcome games.

Image matching is an important task arising in video compression, optical character recognition, medical imaging, watermarking and in many others fields. Given two digital images A and B, image matching determines a transformation f for A such that it most closely resembles B. In this paper, we introduce the first general discretization technique that works for the class of projective transformations

In this contribution we present arbitrary arrow update model logic (AAUML). This is a dynamic epistemic logic or update logic. In update logics, static/basic modalities are interpreted on a given relational model whereas dynamic/update modalities induce transformations (updates) of relational models. In AAUML the update modalities formalize the execution of arrow update models, and there is also a

The Min Label s-t Cut problem is a fundamental problem in combinatorial optimization. This problem comes from many applications in real world, for example, information security and computer networks. We study two linear programs for Min Label s-t Cut, proving that both of them have large integrality gaps, namely, Ω(m) and Ω(m1/3−ϵ) for the respective linear programs, where m is the number of edges

We investigate data-enriched models, like Petri nets with data, where executability of a transition is conditioned by a relation between data values involved. Decidability status of various decision problems in such models may depend on the structure of data domain. According to the WQO Dichotomy Conjecture, if a data domain is homogeneous then it either exhibits a well quasi-order (in which case decidability

Cell-like P systems with symport/antiport rules are computing models inspired by the conservation law, in the sense that they compute by changing the places of objects with respect to the membranes, and not by changing the objects themselves. In this work, a variant of these kinds of membrane systems, called cell-like P systems with evolutional symport/antiport rules, where objects can evolve in the

We present a simple approach for finding all number-conserving two-dimensional cellular automata with the von Neumann neighborhood. We demonstrate the efficiency of this approach by enumerating and describing four special cases: totalistic, outer-totalistic, binary and three-state cellular automata. The last result was not published before. We then proceed to find all reversible two-dimensional number-conserving

Asynchronous Boolean totalistic cellular automata have recently attracted attention as promising models for implementation by reaction-diffusion systems. It is unknown, however, to what extent they are able to conduct computation. In this paper, we introduce the so-called non-camouflage property, which means that a cell's update is insensitive to neighboring states that equal its own state. This property

Cellular automata are discrete dynamical systems with locally defined behaviour, well known as simple models of complex systems. Classically, their dynamics derive from synchronously iterated rules over finite or infinite configurations; however, since for many natural systems to be modelled, asynchrony seems more plausible, asynchronous iteration of the rules has gained a considerable attention in

A set X⊆Σ++ of rectangular pictures over an alphabet Σ is a two-dimensional code if any picture over Σ is tilable in at most one way with pictures in X. Finite strong prefix codes were introduced as a family of decidable two-dimensional codes. We consider infinite strong prefix codes and give a characterization for the maximal ones based on the iterated extensions. Moreover, we study some properties

We consider the asynchronous prediction problem for some automaton as the one consisting in determining, given an initial configuration, if there exists a non-zero probability that some selected site changes its state, when the network is updated picking one site at a time uniformly at random. We show that for the majority automaton, the asynchronous prediction problem is in NC in the two-dimensional

The asynchronous automaton associated with a Boolean network f:{0,1}n→{0,1}n is considered in many applications. It is the finite deterministic automaton with set of states {0,1}n, alphabet {1,…,n}, where the action of letter i on a state x consists in switching the ith component if fi(x)≠xi or doing nothing otherwise. This action is extended to words in the natural way. We then say that a word w fixes

In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells remain unchanged, and the new value of an inactive cell depends only on the sum of its active neighbors. We classify all the Cellular Automata in the class

Let G be a group and A a set. A cellular automaton (CA) τ over AG is von Neumann regular (vN-regular) if there exists a CA σ over AG such that τστ=τ, and in such case, σ is called a weak generalised inverse of τ. In this paper, we investigate the vN-regularity of various kinds of CA. First, we establish that, except for trivial cases, there are always CA that are not vN-regular. Second, we obtain a

Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. Nondeterministic Cellular Automata (NCA) are the class of multi-valued functions obtained by allowing nondeterminism in CA. In this study we extend to multi-valued functions the definition of some important topological properties and investigate the differences between the dynamical behaviour of one-dimensional

Cellular automata are topological dynamical systems. We consider the problem of deciding whether two cellular automata are conjugate or not. We also consider deciding strong conjugacy, that is, conjugacy by a map that commutes with the shift maps. We show that the following two sets of pairs of one-dimensional one-sided cellular automata are recursively inseparable: (i) pairs where the first cellular

Given an n×n sparse symmetric matrix with m nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values, so called fill-ins. The minimum fill-in problem asks whether it is possible to perform the elimination with at most k fill-ins. We exclude the existence of polynomial time approximation schemes for this problem, assuming P≠NP, and the existence of 2O(n1−δ)-time approximation

We introduce compact and succinct representations of a d-dimensional point set for any constant d≥3 supporting orthogonal range searching. Our first data structure uses dnlg⁡n+o(nlg⁡n) bits, where n denotes the number of points in P, and supporting reporting queries in O((n(d−2)/d+occ)lg⁡n/lg⁡lg⁡n) time, and counting queries in O(n(d−2)/dlg⁡n/lg⁡lg⁡n) time, where occ denotes the number of point to

We present a pointer-based data structure for constant time traversal of the edges of an edge-labeled (alphabet Σ) directed hypergraph (a graph where edges can be incident to more than two vertices, and the incident vertices are ordered) given as hyperedge-replacement grammar G. It is assumed that the grammar has a fixed rank κ (maximal number of vertices connected to a nonterminal hyperedge) and that

We present a novel compressed dynamic self-index for highly repetitive text collections. ESP-index is a static self-index of this type and has a large disadvantage of slow pattern search for short patterns. We obtain faster pattern search by leveraging the idea behind a truncated suffix tree (TST) to develop the first compressed dynamic self-index, called TST-index, that supports not only fast pattern

Recent advances in the analysis of random linear systems on finite fields have paved the way for the construction of constant-time data structures representing static functions and minimal perfect hash functions using less space with respect to existing techniques. The main obstacle for any practical application of these results is the time required to solve such linear systems: despite they can be

Existing parallel algorithms for wavelet tree construction have a work complexity of O(nlog⁡σ). This paper presents parallel algorithms for the problem with improved work complexity. Our first algorithm is based on parallel integer sorting and has either O(nlog⁡log⁡n⌈log⁡σ/log⁡nlog⁡log⁡n⌉) work and polylogarithmic depth, or O(n⌈log⁡σ/log⁡n⌉) work and sub-linear depth. We also describe another algorithm

We present a new streaming algorithm for the k-Mismatch problem, one of the most basic problems in pattern matching. Given a pattern and a text, the task is to find all substrings of the text that are at the Hamming distance at most k from the pattern. Our algorithm is enhanced with an important new feature called Error Correcting, and its complexities for k=1 and for a general k are comparable to

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question by presenting a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the resulting delay-free game admits a finite-state strategy. The framework is applicable to games whose winning condition is recognized by an automaton with an acceptance

Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints over a finite set of parameters. Important tasks in the analysis of parametric Markov chains are (1) computing closed-form solutions for reachability probabilities and

We introduce McCarthy-Kleene fuzzy automata (MK-fuzzy automata) over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic. Our automata are inspired by, and intend to contribute to, practical applications being in development in a project on runtime network monitoring based on predicate logic. We investigate closure properties of the class of recognizable MK-fuzzy languages

We consider n-player non-zero sum games played on finite trees (i.e., sequential games), in which the players have the right to repeatedly update their respective strategies. This generates a dynamics in the game which may eventually stabilise to a Nash Equilibrium, and we study the conditions that guarantee such a dynamics to terminate. We build on the works of Le Roux and Pauly who have studied the

The McNaughton-Zielonka divide et impera algorithm is the simplest and most flexible approach available in the literature for determining the winner in a parity game. Despite its theoretical exponential worst-case complexity and the negative reputation as a poorly effective algorithm in practice, it has been shown to rank among the best techniques for solving such games. Also, it proved to be resistant

In this paper, we investigate the model checking (MC) problem for Halpern and Shoham's modal logic of time intervals (HS) and its fragments, where labeling of intervals is defined by regular expressions. The MC problem for HS has recently emerged as a viable alternative to the traditional (point-based) temporal logic MC. Most expressiveness and complexity results have been obtained by imposing suitable

In this paper, we propose to extend First-Order Linear-time Temporal Logic with Past adding two operators “at next” and “at last”, which take in input a term and a formula and return the value of the term at the next state in the future or last state in the past in which the formula holds. The new logic, named LTL-EF, can be interpreted with different models of time (including discrete, dense, and

We investigate the decidability of the emptiness problem for three classes of distributed automata. These devices operate on finite directed graphs, acting as networks of identical finite-state machines that communicate in an infinite sequence of synchronous rounds. The problem is shown to be decidable in LogSpace for a class of forgetful automata, where the nodes see the messages received from their

We show that there exists a bitsequence that is not computably random for which the odd bits are computably random and the even bits are computably random relative to the odd bits.

There are two fundamentally different approaches for specifying and verifying properties of systems. The logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms; the behavioural approach exploits various equivalence or refinement checking methods, provided the specifications are given in the same formalism as implementations

In spite of wide investigations of finite splicing systems in formal language theory, basic questions, such as their characterization, remain unsolved. It has been conjectured that a necessary condition for a regular language L to be a splicing language is that L must have a constant in the Schutzenberger sense. We prove this longstanding conjecture to be true. The result is based on properties of

In this work we present a formalization, backed with a contrasted implementation, of a relational database language (called HR-SQL) that extends SQL in two aspects. On the one hand, including non-linear and mutual recursion. On the other hand, including hypothetical relations and queries. Regarding expressiveness, HR-SQL allows a novel form of hypothetical reasoning, completely integrated with recursive

Functional decomposition is the process of resolving a functional relationship into its constituent parts in such a way that the original function can be recomposed from those parts by functional composition. Perfect decomposition requires the obtained constituent parts to be non-interacting components and easier to conceive, understand, program, and maintain. However, how to decompose a complex system

We study multidimensional configurations (infinite words) and subshifts of low pattern complexity using tools of algebraic geometry. We express the configuration as a multivariate formal power series over integers and investigate the setup when there is a non-trivial annihilating polynomial: a non-zero polynomial whose formal product with the power series is zero. Such annihilator exists, for example

A Petri net is called fork-attribution if it is choice-free (a unique output transition for each place) and join-free (a unique input place for each transition). Synthesis tries, for a given (finite) labelled transition system (LTS), to find an (unlabelled) Petri net with an isomorphic reachability graph. Synthesis often requires a large set of inequality systems to be solved, making it quite costly

Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful ‘separable’ strategy, in the sense that it does not use the winnings from betting on red in order to bet on black, and vice-versa? We study this question from an algorithmic point of view and observe that every strategy M can be replaced by a separable

We study the relations between the notions of highness, lowness and logical depth in the setting of complexity theory. We introduce a new notion of polylog depth based on time bounded Kolmogorov complexity. We show polylog depth satisfies all basic logical depth properties, namely sets in P are not polylog deep, sets with (time bounded)-Kolmogorov complexity greater than polylog are not polylog deep

Let S=(V,f), be a symmetric submodular system. For two distinct elements s and l of V, let Γ(s,l) denote the set of all subsets of V which separate s from l. By using any Gomory-Hu tree of S we can obtain an element of Γ(s,l) which has minimum value among all the elements of Γ(s,l). This tree can be constructed iteratively by solving |V|−1 minimum sl−separator problem. Pendant pairs of a symmetric

The study of computing in presence of faulty robots in the Look-Compute-Move model has been the object of extensive investigation, typically to design fault-tolerant algorithms. In this paper, we initiate a new line of investigation on the presence of faults, focusing on a different issue: we study, for the first time, the unintended dynamics of the robots when they execute an algorithm designed for

This paper contributes to a generic theory of behaviour of “finite-state” systems. Systems are coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category. Their behaviour gives rise to the locally finite fixpoint (LFF), a new fixpoint of the endofunctor. The LFF exists provided that the endofunctor is finitary and preserves monomorphisms, is a subcoalgebra