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Reachability for Bounded Branching VASSApr 23 2019In this paper we consider the reachability problem for bounded branching VASS. Bounded VASS are a variant of the classic VASS model where all values in all configurations are upper bounded by a fixed natural number, encoded in binary in the input. This ... More

A general architecture of oritatami systems for simulating arbitrary finite automataApr 23 2019In this paper, we propose an architecture of oritatami systems with which one can simulate an arbitrary nondeterministic finite automaton (NFA) in a unified manner. The oritatami system is known to be Turing-universal but the simulation available so far ... More

The undirected repetition thresholdApr 22 2019For rational $1<r\leq 2$, an undirected $r$-power is a word of the form $xyx'$, where $x\neq \varepsilon$, $x'\in\{x,x^R\}$, and $|xyx'|/|xy|=r$. The undirected repetition threshold for $k$ letters, denoted $\mathrm{URT}(k)$, is the infimum of the set ... More

Repetitions in infinite palindrome-rich wordsApr 22 2019Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting open problems. ... More

Translating between models of concurrencyApr 22 2019Hoare's Communicating Sequential Processes (CSP) admits a rich universe of semantic models closely related to the van Glabbeek spectrum. In this paper we study finite observational models, of which at least six have been identified for CSP, namely traces, ... More

Linear Bounded Composition of Tree-Walking Tree Transducers: Linear Size Increase and ComplexityApr 19 2019Compositions of tree-walking tree transducers form a hierarchy with respect to the number of transducers in the composition. As main technical result it is proved that any such composition can be realized as a linear bounded composition, which means that ... More

New results on pseudosquare avoidanceApr 19 2019We start by considering binary words containing the minimum possible numbers of squares and antisquares (where an antisquare is a word of the form $x \overline{x}$), and we completely classify which possibilities can occur. We consider avoiding $x p(x)$, ... More

Preservation of normality by transducersApr 19 2019We consider input-deterministic finite state transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality on infinite words. When these transducers are given by a strongly connected set of states, and when the ... More

k-Spectra of c-Balanced WordsApr 19 2019A word $u$ is a scattered factor of $w$ if $u$ can be obtained from $w$ by deleting some of its letters. That is, there exist the (potentially empty) words $u_1,u_2,..., u_n$, and $v_0,v_1,..,v_n$ such that $u = u_1u_2...u_n$ and $w = v_0u_1v_1u_2v_2...u_nv_n$. ... More

Parametric updates in parametric timed automataApr 18 2019We introduce a new class of Parametric Timed Automata (PTAs) where we allow clocks to be compared to parameters in guards, as in classic PTAs, but also to be updated to parameters. We focus here on the EF-emptiness problem: "is the set of parameter valuations ... More

Tree Automata as Algebras: Minimisation and DeterminisationApr 18 2019We study a categorical generalisation of tree automata, as $\Sigma$-algebras for a fixed endofunctor $\Sigma$ endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm for these ... More

Undecidability of future timeline-based planning over dense temporal domainsApr 18 2019Planning is one of the most studied problems in computer science. In this paper, we consider the timeline-based approach, where the domain is modeled by a set of independent, but interacting, components, identified by a set of state variables, whose behavior ... More

Fast algorithms for handling diagonal constraints in timed automataApr 18 2019A popular method for solving reachability in timed automata proceeds by enumerating reachable sets of valuations represented as zones. A na\"ive enumeration of zones does not terminate. Various termination mechanisms have been studied over the years. ... More

Re-pairing bracketsApr 17 2019Consider the following one-player game. Take a well-formed sequence of opening and closing brackets. As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the entire sequence, ... More

Circularly squarefree words and unbordered conjugates: a new approachApr 17 2019Using a new approach based on automatic sequences, logic, and a decision procedure, we reprove some old theorems about circularly squarefree words and unbordered conjugates in a new and simpler way. Furthermore, we prove three new results about unbordered ... More

The many roads to the simulation of reaction systemsApr 15 2019Reaction systems are a computational model inspired by the bio-chemical reactions that happen inside biological cells. They have been and currently are studied for their many nice theoretical properties. They are also a useful modeling tool for biochemical ... More

Non-Sequential Theory of Distributed SystemsApr 15 2019These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over words, which provide ... More

Matrix approach to synchronizing automataApr 13 2019A word $w$ of letters on edges of underlying graph $\Gamma$ of deterministic finite automaton (DFA) is called synchronizing if $w$ sends all states of the automaton to a unique state. J. \v{C}erny discovered in 1964 a sequence of $n$-state complete DFA ... More

Transforming opacity verification to nonblocking verification in modular systemsApr 12 2019We consider the verification of current-state and K-step opacity for systems modeled as interacting non-deterministic finite-state automata. We describe a new methodology for compositional opacity verification that employs abstraction, in the form of ... More

On Functions Weakly Computable by Pushdown Petri Nets and Related SystemsApr 08 2019We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions $F_\alpha$ for $\alpha<\omega^\omega$, hence they are computationally ... More

Attack-Resilient Supervisory Control of Discrete-Event SystemsApr 05 2019In this work, we study the problem of supervisory control of discrete-event systems (DES) in the presence of attacks that tamper with inputs and outputs of the plant. We consider a very general system setup as we focus on both deterministic and nondeterministic ... More

Computational Limitations of Affine AutomataApr 04 2019We present two new results on the computational limitations of affine automata. First, we show that the computation of bounded-error rational-values affine automata is simulated in logarithmic space. Second, we give an impossibility result for algebraic-valued ... More

On the Formalization of Importance Measures using HOL Theorem ProvingApr 02 2019Importance measures provide a systematic approach to scrutinize critical system components, which are extremely beneficial in making important decisions, such as prioritizing reliability improvement activities, identifying weak-links and effective usage ... More

Complete Abstractions for Checking Language InclusionApr 02 2019We study the language inclusion problem $L_1 \subseteq L_2$ where $L_1$ is regular or context-free. Our approach relies on abstract interpretation and checks whether an overapproximating abstraction of $L_1$, obtained by successively overapproximating ... More

The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpointsApr 02 2019It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized language with ... More

Bisimulation for Feller-Dynkin ProcessesApr 01 2019Bisimulation is a concept that captures behavioural equivalence. It has been studied extensively on nonprobabilistic systems and on discrete-time Markov processes and on so-called continuous-time Markov chains. In the latter time is continuous but the ... More

Boundedness of Conjunctive Regular Path QueriesApr 01 2019We study the boundedness problem for unions of conjunctive regular path queries with inverses (UC2RPQs). This is the problem of, given a UC2RPQ, checking whether it is equivalent to a union of conjunctive queries (UCQ). We show the problem to be ExpSpace-complete, ... More

Liveness in Broadcast NetworksApr 01 2019We study two liveness verification problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem is liveness verification. It asks whether there is a computation such that one of the clients ... More

Alternating Weak Automata from Universal TreesMar 29 2019An improved translation from alternating parity automata on infinite words to alternating weak automata is given. The blow-up of the number of states is related to the size of the smallest universal ordered trees and hence it is quasi-polynomial, and ... More

Generic properties in some classes of automaton groupsMar 27 2019We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order. In certain cases, it also implies other results such as exponential growth.

Partitioning a Symmetric Rational Relation into Two Asymmetric Rational RelationsMar 26 2019We consider the problem of partitioning effectively a given symmetric (and irreflexive) rational relation R into two asymmetric rational relations. This problem is motivated by a recent method of embedding an R-independent language into one that is maximal ... More

Using Sat solvers for synchronization issues in partial deterministic automataMar 25 2019We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that this approach ... More

Context-free word problem semigroupsMar 25 2019This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the notions of word-hyperbolicity ... More

A Characterization of Morphic Words with Polynomial GrowthMar 24 2019A morphic word is obtained by iterating a morphism to generate an infinite word, and then applying a coding. We characterize morphic words with polynomial growth in terms of a new type of infinite word called a $\textit{zigzag word}$. A zigzag word is ... More

Effective Definability of the Reachability Relation in Timed AutomataMar 23 2019We give a new proof of the result of Comon and Jurski that the binary reachability relation of a timed automaton is definable in linear arithmetic.

Varieties of Data LanguagesMar 19 2019We establish an Eilenberg-type correspondence for data languages, i.e. languages over an infinite alphabet. More precisely, we prove that there is a bijective correspondence between varieties of languages recognized by orbit-finite nominal monoids and ... More

Complexity of the dynamics of reaction systemsMar 19 2019Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena that complements ... More

One-Way Topological Automata and the Tantalizing Effects of Their Topological FeaturesMar 18 2019We cast new light on the existing models of 1-way deterministic topological automata by introducing a new, convenient model, in which, as each input symbol is read, an interior system of an automaton, known as a configuration, continues to evolve in a ... More

Online Parametric Timed Pattern Matching with Automata-Based SkippingMar 18 2019Timed pattern matching has strong connections with monitoring real-time systems. Given a log and a specification containing timing parameters (that can capture uncertain or unknown constants), parametric timed pattern matching aims at exhibiting for which ... More

LIKE Patterns and ComplexityMar 14 2019We investigate the expressive power and complexity questions for the LIKE operator in SQL.

On Finite $1$-Dimensional Cellular Automata: Reversibility and Semi-reversibilityMar 14 2019Reversibility of a one-dimensional finite cellular automaton (CA) is dependent on lattice size. A finite CA can be reversible for a set of lattice sizes. On the other hand, reversibility of an infinite CA, which is decided by exploring the rule only, ... More

Regular Expressions with Backreferences: Polynomial-Time Matching TechniquesMar 14 2019Regular expressions with backreferences (regex, for short), as supported by most modern libraries for regular expression matching, have an NP-complete matching problem. We define a complexity parameter of regex, called active variable degree, such that ... More

Generalized de Bruijn words and the state complexity of conjugate setsMar 13 2019We consider a certain natural generalization of de Bruijn words, and use it to compute the exact maximum state complexity for the language consisting of the conjugates of a single word.

The relationship between word complexity and computational complexity in subshiftsMar 11 2019We prove several results about the relationship between the word complexity function of a subshift and the set of Turing degrees of points of the subshift, which we call the Turing spectrum. Among other results, we show that a Turing spectrum can be realized ... More

State complexity of the multiples of the Thue-Morse setMar 10 2019The Thue-Morse set is the set of those nonnegative integers whose binary expansions have an even number of $1$. We obtain an exact formula for the state complexity of the multiplication by a constant of the Thue-Morse set $\mathcal{T}$ with respect with ... More

Native Chemical Automata and the Thermodynamic Interpretation of Their Experimental Accept/Reject ResponsesMar 09 2019The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language classes. The ... More

Insertion Operations on Deterministic Reversal-Bounded Counter MachinesMar 08 2019Several insertion operations are studied applied to languages accepted by one-way and two-way deterministic reversal-bounded multicounter machines. These operations are defined by the ideals obtained from relations such as the prefix, infix, suffix, and ... More

On counting functions and slenderness of languagesMar 08 2019We study counting-regular languages -- these are languages $L$ for which there is a regular language $L'$ such that the number of strings of length $n$ in $L$ and $L'$ are the same for all $n$. We show that the languages accepted by unambiguous nondeterministic ... More

On the Density of Languages Accepted by Turing Machines and Other Machine ModelsMar 07 2019A language is dense if the set of all infixes (or subwords) of the language is the set of all words. Here, it is shown that it is decidable whether the language accepted by a nondeterministic Turing machine with a one-way read-only input and a reversal-bounded ... More

On the Density of Context-Free and Counter LanguagesMar 07 2019A language $L$ is said to be dense if every word in the universe is an infix of some word in $L$. This notion has been generalized from the infix operation to arbitrary word operations $\varrho$ in place of the infix operation ($\varrho$-dense, with infix-dense ... More

Invariant Safety for Distributed ApplicationsMar 07 2019We study a proof methodology for verifying the safety of data invariants of highly-available distributed applications that replicate state. The proof is (1) modular: one can reason about each individual operation separately, and (2) sequential: one can ... More

Nonlinear Craig Interpolant GenerationMar 04 2019Mar 05 2019Interpolation-based techniques have become popularized in recent years because of their inherently modular and local reasoning, which can scale up existing formal verification techniques like theorem proving, model-checking, abstraction interpretation, ... More

Monadic Decomposability of Regular RelationsMar 02 2019Mar 07 2019Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical theory. In this ... More

Monadic Decomposability of Regular RelationsMar 02 2019Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical theory. In this ... More

A Trichotomy for Regular Trail QueriesMar 01 2019Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order ... More

Orbits of Automaton Semigroups and GroupsMar 01 2019We study the orbits of right infinite or $\omega$-words under the action of semigroups and groups generated by automata. We see that an automaton group or semigroup is infinite if and only if it admits an $\omega$-word with an infinite orbit, which solves ... More

Sequentiality of String-to-Context TransducersFeb 28 2019Transducers extend finite state automata with outputs, and describe transformations from strings to strings. Sequential transducers, which have a deterministic behaviour regarding their input, are of particular interest. However, unlike finite-state automata, ... More

Register GamesFeb 27 2019The complexity of parity games is a long standing open problem that saw a major breakthrough in 2017 when two quasi-polynomial algorithms were published. The present article presents a third, independent approach to solving parity games in quasi-polynomial ... More

Register GamesFeb 27 2019Feb 28 2019The complexity of parity games is a long standing open problem that saw a major breakthrough in 2017 when two quasi-polynomial algorithms were published. The present article presents a third, independent approach to solving parity games in quasi-polynomial ... More

Representing Formal Languages: A Comparison Between Finite Automata and Recurrent Neural NetworksFeb 27 2019We investigate the internal representations that a recurrent neural network (RNN) uses while learning to recognize a regular formal language. Specifically, we train a RNN on positive and negative examples from a regular language, and ask if there is a ... More

On reachability problems for low dimensional matrix semigroupsFeb 25 2019We consider the Membership and the Half-space Reachability Problems for matrices in dimensions two and three. Our first main result is that the Membership Problem is decidable for fintely generated sub-semigroups of the Heisenberg group over integer numbers. ... More

Polynomially Ambiguous Probabilistic Automata on Restricted LanguagesFeb 25 2019We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for non strict cutpoints of polynomially ambiguous PFA remains undecidable even ... More

The computational power of parsing expression grammarsFeb 21 2019We study the computational power of parsing expression grammars (PEGs). We begin by constructing PEGs with unexpected behaviour, and surprising new examples of languages with PEGs, including the language of palindromes whose length is a power of two, ... More

Aperiodic Weighted Automata and Weighted First-Order LogicFeb 21 2019By fundamental results of Sch\"utzenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata form a general ... More

A complete axiomatisation of reversible Kleene latticesFeb 21 2019We consider algebras of languages over the signature of reversible Kleene lattices, that is the regular operations (empty and unit languages, union, concatenation and Kleene star) together with intersection and mirror image. We provide a complete set ... More

Emergence of order in random languagesFeb 20 2019We consider languages generated by weighted context-free grammars. It is shown that the behaviour of large texts is controlled by saddle-point equations for an appropriate generating function. We then consider ensembles of grammars, in particular the ... More

On Termination of Integer Linear LoopsFeb 20 2019We consider the problem of determining termination of single-path loops with integer variables and affine updates. The problem asks whether such a loop terminates on all integer initial values. This problem is known to be decidable for the subclass of ... More

Query Learning Algorithm for Residual Symbolic Finite AutomataFeb 20 2019Feb 21 2019We propose a query learning algorithm for residual symbolic finite automata (RSFAs). A symbolic finite automaton (SFA) is a finite automata whose transitions are labeled by predicates over a Boolean algebra, in which a big bunch of characters leading ... More

Solutions sets to systems of equations in hyperbolic groups are EDT0L in PSPACEFeb 19 2019We show that the full set of solutions to systems of equations and inequations in a hyperbolic group, with or without torsion, as shortlex geodesic words, is an EDT0L language whose specification can be computed in $\mathsf{NSPACE}(n^2\log n)$ for the ... More

Lower bounds on separation automata for Parity GamesFeb 19 2019Several recently developed quasi-polynomial time algorithms for Parity Games rely on construction of an automaton with quasi-polynomial number of states that separates specific languages of infinite words. This motivates a question of whether a matching ... More

Taking-and-merging games as rewrite gamesFeb 19 2019This work contributes to the study of rewrite games where positions are words and the moves are local rewriting rules of the form u->v belonging to a finite set. We introduce and investigate taking-and-merging games where each rule is of the form a^k->epsilon. ... More

On the dynamical behaviour of linear higher-order cellular automata and its decidabilityFeb 18 2019Higher-order cellular automata (HOCA) are a variant of cellular automata (CA) used in many applications (ranging, for instance, from the design of secret sharing schemes to data compression and image processing), and in which the global state of the system ... More

Complexity of the Frobenius monoid problem for a finite languageFeb 18 2019Feb 20 2019We solve an open problem concerning the computational complexity of the Frobenius monoid problem for a finite language. We show that determining whether for a finite language $L$ over an alphabet $\Sigma$ represented as a list of words, the language $L^*$ ... More

Complexity of the Frobenius monoid problem for a finite languageFeb 18 2019We solve an open problem concerning the computational complexity of the Frobenius monoid problem for a finite language. We show that determining whether for a finite language $L$ over an alphabet $\Sigma$ represented as a list of words, the language $L^*$ ... More

Relational parsing: a clean, fast parsing strategy for all context-free languagesFeb 18 2019We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state of the art: ... More

A Lower Bound for Primality of Finite LanguagesFeb 17 2019A regular language $L$ is said to be prime, if it is not the product of two non-trivial languages. Martens et al. settled the exact complexity of deciding primality for deterministic finite automata in 2010. For finite languages, Mateescu et al. and Wieczorek ... More

Finite test sets for morphisms which are square-free on some of Thue's square-free ternary wordsFeb 15 2019Let $S$ be one of $\{aba,bcb\}$ and $\{aba, aca\}$, and let $w$ be an infinite square-free word over $\Sigma=\{a,b,c\}$ with no factor in $S$. Suppose that $f:\Sigma\rightarrow T^*$ is a non-erasing morphism. Word $f(w)$ is square-free if and only if ... More

Continuous Reachability for Unordered Data Petri nets is in PTimeFeb 14 2019Unordered data Petri nets (UDPN) are an extension of classical Petri nets with tokens that carry data from an infinite domain and where transitions may check equality and disequality of tokens. UDPN are well-structured, so the coverability and termination ... More

On long words avoiding Zimin patternsFeb 14 2019A pattern is encountered in a word if some infix of the word is the image of the pattern under some non-erasing morphism. A pattern $p$ is unavoidable if, over every finite alphabet, every sufficiently long word encounters $p$. A theorem by Zimin and ... More

Complexity-Theoretic Aspects of Expanding Cellular AutomataFeb 14 2019The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. The respective polynomial-time complexity class is shown to coincide with ${\le_{tt}^p}(\textbf{NP})$, that ... More

Slowly synchronizing DFAs of 7 states and maximal slowly synchronizing DFAsFeb 14 2019We compute all synchronizing DFAs with 7 states and synchronization length >= 29. Furthermore, we compute alphabet size ranges for maximal, minimal and semi-minimal synchronizing DFAs with up to 7 states.

HyPLC: Hybrid Programmable Logic Controller Program Translation for VerificationFeb 14 2019Programmable Logic Controllers (PLCs) provide a prominent choice of implementation platform for safety-critical industrial control systems. Formal verification provides ways of establishing correctness guarantees, which can be quite important for such ... More

The Cost of Monitoring AloneFeb 13 2019We compare the succinctness of two monitoring systems for properties of infinite traces, namely parallel and regular monitors. Although a parallel monitor can be turned into an equivalent regular monitor, the cost of this transformation is a double-exponential ... More

Separation and covering for group based concatenation hierarchiesFeb 13 2019Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations. Concatenation hierarchies ... More

Security-Aware Synthesis Using Delayed-Action GamesFeb 12 2019Stochastic multiplayer games (SMGs) have gained attention in the field of strategy synthesis for multi-agent reactive systems. However, standard SMGs are limited to modeling systems where all agents have full knowledge of the state of the game. In this ... More

Statistical Model Checking for Probabilistic HyperpropertiesFeb 11 2019Feb 13 2019In this paper, we propose the temporal logic HyperPCTL$^*$ that extends PCTL$^*$ and HyperPCTL to reason about probabilistic hyperproperties. It allows expressing probabilistic hyperproperties with nested temporal and probability operators. We show that ... More

Statistical Model Checking for Probabilistic HyperpropertiesFeb 11 2019In this paper, we propose the temporal logic HyperPCTL$^*$ that extends PCTL$^*$ and HyperPCTL to reason about probabilistic hyperproperties. It allows expressing probabilistic hyperproperties with nested temporal and probability operators. We show that ... More

Deciding Equivalence of Separated Non-Nested Attribute Systems in Polynomial TimeFeb 11 2019In 1982, Courcelle and Franchi-Zannettacci showed that the equivalence problem of separated non-nested attribute systems can be reduced to the equivalence problem of total deterministic separated basic macro tree transducers. They also gave a procedure ... More

Structural Invariants for Parametric Verification of Systems with Almost Linear ArchitecturesFeb 07 2019We consider concurrent systems consisting of a finite but unknown number of components, that are replicated instances of a given set of finite state automata. The components communicate by executing interactions which are simultaneous atomic state changes ... More

Walking on SR-automata to detect grammar ambiguityFeb 07 2019We exploit the nondeterminism of LR parsing tables to reason about grammar ambiguity after a conflict-driven strategy. First, from parsing tables we define specialized structures, called SR-automata. Next, we search for ambiguous words along the paths ... More

Determinization of Büchi Automata: Unifying the Approaches of Safra and Muller-SchuppFeb 06 2019Determinization of B\"uchi automata is a long-known difficult problem and after the seminal result of Safra, who developed the first asymptotically optimal construction from B\"uchi into Rabin automata, much work went into improving, simplifying or avoiding ... More

Modeling Terms by Graphs with Structure Constraints (Two Illustrations)Feb 06 2019In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing questions about ... More

A Session Type System for Asynchronous Unreliable Broadcast CommunicationFeb 04 2019Session types are formal specifications of communication protocols, allowing protocol implementations to be verified by typechecking. Up to now, session type disciplines have assumed that the communication medium is reliable, with no loss of messages. ... More

The number of languages with maximum state complexityFeb 02 2019Champarnaud and Pin (1989) found that the minimal deterministic automaton of a language $L\subset\Sigma^n$, where $\Sigma=\{0,1\}$, has at most \[ \sum_{i=0}^n \min(2^i, 2^{2^{n-i}}-1) \] states, and for each $n$ there exists $L$ attaining this bound. ... More

Planar digraphs for automatic complexityFeb 02 2019We show that the digraph of a nondeterministic finite automaton witnessing the automatic complexity of a word can always be taken to be planar. In the case of total transition functions studied by Shallit and Wang, planarity can fail. Let $s_q(n)$ be ... More

Critical exponent of infinite balanced words via the Pell number systemFeb 01 2019In a recent paper of Rampersad et al., the authors conjectured that the smallest possible critical exponent of an infinite balanced word over a 5-letter alphabet is $3/2$. We prove this result, using a formulation of first-order logic, the Pell number ... More

On the effects of firing memory in the dynamics of conjunctive networksJan 28 2019Boolean networks are one of the most studied discrete models in the context of the study of gene expression. In order to define the dynamics associated to a Boolean network, there are several \emph{update schemes} that range from parallel or \emph{synchronous} ... More

A model for a Lindenmayer reconstruction algorithmJan 24 2019Given an input string s and a specific Lindenmayer system (the so-called Fibonacci grammar), we define an automaton which is capable of (i) determining whether s belongs to the set of strings that the Fibonacci grammar can generate (in other words, if ... More

Reachability Problem in Non-uniform Cellular AutomataJan 24 2019This paper deals with the CREP (Configuration REachability Problem) for non-uniform cellular automata (CAs). The cells of non-uniform CAs, we have considered here, can use different Wolfram's rules to generate their next states. We report an algorithm ... More

Palindromic Subsequences in Finite WordsJan 22 2019In 1999 Lyngs{\o} and Pedersen proposed a conjecture stating that every binary circular word of length $n$ with equal number of zeros and ones has an antipalindromic linear subsequence of length at least $\frac{2}{3}n$. No progress over a trivial $\frac{1}{2}n$ ... More