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Improved Randomized Approximation of Hard Universality and Emptiness Problems arXiv.cs.FL Pub Date : 2024-03-13 Pantelis Andreou, Stavros Konstantinidis, Taylor J. Smith
We build on recent research on polynomial randomized approximation (PRAX) algorithms for the hard problems of NFA universality and NFA equivalence. Loosely speaking, PRAX algorithms use sampling of infinite domains within any desired accuracy $\delta$. In the spirit of experimental mathematics, we extend the concept of PRAX algorithms to be applicable to the emptiness and universality problems in any
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Semidirect Product Decompositions for Periodic Regular Languages arXiv.cs.FL Pub Date : 2024-03-08 Yusuke Inoue, Kenji Hashimoto, Hiroyuki Seki
The definition of period in finite-state Markov chains can be extended to regular languages by considering the transitions of DFAs accepting them. For example, the language $(\Sigma\Sigma)^*$ has period two because the length of a recursion (cycle) in its DFA must be even. This paper shows that the period of a regular language appears as a cyclic group within its syntactic monoid. Specifically, we
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Characterizations of Controlled Generation of Right Linear Grammars with Unknown Behaviors arXiv.cs.FL Pub Date : 2024-03-07 Daihei Ise, Satoshi Kobayashi
This paper deals with the control generation of right linear grammars with unknown behaviors (RLUBs, for short) in which derivation behavior is not determined completely. In particular, we consider a physical property of control devices used in control systems and formulate it as a partial order over control alphabet of the control system. We give necessary and sufficient conditions for given finite
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Enumeration for MSO-Queries on Compressed Trees arXiv.cs.FL Pub Date : 2024-03-05 Markus Lohrey, Markus L. Schmid
We present a linear preprocessing and output-linear delay enumeration algorithm for MSO-queries over trees that are compressed in the well-established grammar-based framework. Time bounds are measured with respect to the size of the compressed representation of the tree. Our result extends previous work on the enumeration of MSO-queries over uncompressed trees and on the enumeration of document spanners
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Efficient Interaction-Based Offline Runtime Verification of Distributed Systems with Lifeline Removal arXiv.cs.FL Pub Date : 2024-03-05 Erwan Mahe, Boutheina Bannour, Christophe Gaston, Pascale Le Gall
Runtime Verification (RV) refers to a family of techniques in which system executions are observed and confronted to formal specifications, with the aim of identifying faults. In Offline RV, observation is done in a first step and verification in a second, on a static artifact collected during observation. In this paper, we define an approach to offline RV of Distributed Systems (DS) against interactions
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Around Don's conjecture for binary completely reachable automata arXiv.cs.FL Pub Date : 2024-02-29 Yinfeng Zhu
A word $w$ is called a reaching word of a subset $S$ of states in a deterministic finite automaton (DFA) if $S$ is the image of $Q$ under the action of $w$. A DFA is called completely reachable if every non-empty subset of the state set has a reaching word. A conjecture states that in every $n$-state completely reachable DFA, for every $k$-element subset of states, there exists a reaching word of length
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Computing Minimal Absent Words and Extended Bispecial Factors with CDAWG Space arXiv.cs.FL Pub Date : 2024-02-28 Shunsuke Inenaga, Takuya Mieno, Hiroki Arimura, Mitsuru Funakoshi, Yuta Fujishige
A string $w$ is said to be a minimal absent word (MAW) for a string $S$ if $w$ does not occur in $S$ and any proper substring of $w$ occurs in $S$. We focus on non-trivial MAWs which are of length at least 2. Finding such non-trivial MAWs for a given string is motivated for applications in bioinformatics and data compression. Fujishige et al. [TCS 2023] proposed a data structure of size $\Theta(n)$
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Specifying and Verifying the Convergence Stairs of the Collatz Program arXiv.cs.FL Pub Date : 2024-02-29 Ali Ebnenasir
This paper presents an algorithmic method that, given a positive integer $j$, generates the $j$-th convergence stair containing all natural numbers from where the Collatz conjecture holds by exactly $j$ applications of the Collatz function. To this end, we present a novel formulation of the Collatz conjecture as a concurrent program, and provide the general case specification of the $j$-th convergence
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Regular Languages in the Sliding Window Model arXiv.cs.FL Pub Date : 2024-02-20 Moses Ganardi, Danny Hucke, Markus Lohrey, Konstantinos Mamouras, Tatiana Starikovskaya
We study the space complexity of the following problem: For a fixed regular language $L$, test membership of a sliding window of length $n$ to $L$ over a given stream of symbols. For deterministic streaming algorithms we prove a trichotomy theorem, namely that the (optimal) space complexity is either constant, logarithmic or linear, measured in the window length $n$. Additionally, we provide natural
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Kleene Theorems for Lasso Languages and $ω$-Languages arXiv.cs.FL Pub Date : 2024-02-20 Mike Cruchten
Automata operating on pairs of words were introduced as an alternative way of capturing acceptance of regular $\omega$-languages. Families of DFAs and lasso automata operating on such pairs followed, giving rise to minimisation algorithms, a Myhill-Nerode theorem and language learning algorithms. Yet Kleene theorems for such a well-established class are still missing. Here, we introduce rational lasso
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Attack Tree Generation via Process Mining arXiv.cs.FL Pub Date : 2024-02-19 Alyzia-Maria Konsta, Gemma Di Federico, Alberto Lluch Lafuente, Andrea Burattin
Attack Trees are a graphical model of security used to study threat scenarios. While visually appealing and supported by solid theories and effective tools, one of their main drawbacks remains the amount of effort required by security experts to design them from scratch. This work aims to remedy this by providing a method for the automatic generation of Attack Trees from attack logs. The main original
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Temporal hierarchies of regular languages arXiv.cs.FL Pub Date : 2024-02-15 Thomas Place, Marc Zeitoun
We classify the regular languages using an operator $\mathcal{C}\mapsto TL(\mathcal{C})$. For each input class of languages $\mathcal{C}$, it builds a larger class $TL(\mathcal{C})$ consisting of all languages definable in a variant of unary temporal logic whose future/past modalities depend on $\mathcal{C}$. This defines the temporal hierarchy of basis $\mathcal{C}$: level $n$ is built by applying
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Bridging the Empirical-Theoretical Gap in Neural Network Formal Language Learning Using Minimum Description Length arXiv.cs.FL Pub Date : 2024-02-15 Nur Lan, Emmanuel Chemla, Roni Katzir
Neural networks offer good approximation to many tasks but consistently fail to reach perfect generalization, even when theoretical work shows that such perfect solutions can be expressed by certain architectures. Using the task of formal language learning, we focus on one simple formal language and show that the theoretically correct solution is in fact not an optimum of commonly used objectives --
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Flattability of Priority Vector Addition Systems arXiv.cs.FL Pub Date : 2024-02-14 Roland Guttenberg
Vector addition systems (VAS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VAS, which consists of deciding whether a target configuration of a VAS is reachable from a given initial configuration. One of the main approaches to solve the problem on practical instances is called flattening, intuitively removing
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Inform: From Compartmental Models to Stochastic Bounded Counter Machines arXiv.cs.FL Pub Date : 2024-02-14 Tim Leys, Guillermo A. Perez
Compartmental models are used in epidemiology to capture the evolution of infectious diseases such as COVID-19 in a population by assigning members of it to compartments with labels such as susceptible, infected, and recovered. In a stochastic compartmental model the flow of individuals between compartments is determined probabilistically. We establish that certain stochastic compartment models can
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Logical Synchrony Networks: A formal model for deterministic distribution arXiv.cs.FL Pub Date : 2024-02-12 Logan Kenwright, Partha Roop, Nathan Allen, Sanjay Lall, Calin Cascaval, Tammo Spalink, Martin Izzard
Kahn Process Networks (KPNs) are a deterministic Model of Computation (MoC) for distributed systems. KPNs supports non-blocking writes and blocking reads, with the consequent assumption of unbounded buffers between processes. Variants such as Finite FIFO Platforms (FFP) have been developed, which enforce boundedness. One issue with existing models is that they mix process synchronisation with process
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Distributed Fair Assignment and Rebalancing for Mobility-on-Demand Systems via an Auction-based Method arXiv.cs.FL Pub Date : 2024-02-07 Kaier Liang, Cristian-Ioan Vasile
In this paper, we consider fair assignment of complex requests for Mobility-On-Demand systems. We model the transportation requests as temporal logic formulas that must be satisfied by a fleet of vehicles. We require that the assignment of requests to vehicles is performed in a distributed manner based only on communication between vehicles while ensuring fair allocation. Our approach to the vehicle-request
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Fully Generalized Reactivity(1) Synthesis arXiv.cs.FL Pub Date : 2024-02-05 Rüdiger Ehlers, Ayrat Khalimov
Generalized Reactivity(1) (GR(1)) synthesis is a reactive synthesis approach in which the specification is split into two parts: a symbolic game graph, describing the safe transitions of a system, a liveness specification in a subset of Linear Temporal Logic (LTL) on top of it. Many specifications can naturally be written in this restricted form, and the restriction gives rise to a scalable synthesis
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Backward Responsibility in Transition Systems Using General Power Indices arXiv.cs.FL Pub Date : 2024-02-02 Christel Baier, Roxane van den Bossche, Sascha Klüppelholz, Johannes Lehmann, Jakob Piribauer
To improve reliability and the understanding of AI systems, there is increasing interest in the use of formal methods, e.g. model checking. Model checking tools produce a counterexample when a model does not satisfy a property. Understanding these counterexamples is critical for efficient debugging, as it allows the developer to focus on the parts of the program that caused the issue. To this end,
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Deciding Subtyping for Asynchronous Multiparty Sessions arXiv.cs.FL Pub Date : 2024-01-29 Elaine Li, Felix Stutz, Thomas Wies
Multiparty session types (MSTs) are a type-based approach to verifying communication protocols, represented as global types in the framework. We present a precise subtyping relation for asynchronous MSTs with communicating state machines (CSMs) as implementation model. We address two problems: when can a local implementation safely substitute another, and when does an arbitrary CSM implement a global
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Collaboration Petri Nets: Verification, Equivalence, and Discovery (Extended Version) arXiv.cs.FL Pub Date : 2024-01-29 Janik-Vasily Benzin, Stefanie Rinderle-Ma
Process modeling and discovery techniques aim to construct sound and valid process models for different types of processes, i.e., process orchestrations and collaboration processes. Orchestrations represent behavior of cases within one process. Collaboration processes represent behavior of collaborating cases within multiple process orchestrations that interact via collaboration concepts such as organizations
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Dot-depth three, return of the J-class arXiv.cs.FL Pub Date : 2024-01-29 Thomas Place, Marc Zeitoun
We look at concatenation hierarchies of classes of regular languages. Each such hierarchy is determined by a single class, its basis: level $n$ is built by applying the Boolean polynomial closure operator (BPol), $n$ times to the basis. A prominent and difficult open question in automata theory is to decide membership of a regular language in a given level. For instance, for the historical dot-depth
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On the Separability Problem of VASS Reachability Languages arXiv.cs.FL Pub Date : 2024-01-29 Eren Keskin, Roland Meyer
We show that the regular separability problem of VASS reachability languages is decidable and $\mathbf{F}_{\omega}$-complete. At the heart of our decision procedure are doubly-marked graph transition sequences, a new proof object that tracks a suitable product of the VASS we wish to separate. We give a decomposition algorithm for DMGTS that not only achieves perfectness as known from MGTS, but also
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Deterministic Parikh automata on infinite words arXiv.cs.FL Pub Date : 2024-01-26 Mario Grobler, Sebastian Siebertz
Various variants of Parikh automata on infinite words have recently been introduced and studied in the literature. However, with some exceptions only their non-deterministic versions have been studied. In this paper we study the deterministic versions of all variants of Parikh automata on infinite words that have not yet been studied in the literature. We compare the expressiveness of the deterministic
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Bonding Grammars arXiv.cs.FL Pub Date : 2024-01-25 Tikhon Pshenitsyn
We introduce bonding grammars, a graph grammar formalism developed to model DNA computation by means of graph transformations. It is a modification of fusion grammars introduced by Kreowski, Kuske and Lye in 2017. Bonding is a graph transformation that consists of merging two hyperedges into a single larger one. We show why bonding better reflects interaction between DNA molecules than fusion. We prove
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Scalable Tree-based Register Automata Learning arXiv.cs.FL Pub Date : 2024-01-25 Simon Dierl, Paul Fiterau-Brostean, Falk Howar, Bengt Jonsson, Konstantinos Sagonas, Fredrik Tåquist
Existing active automata learning (AAL) algorithms have demonstrated their potential in capturing the behavior of complex systems (e.g., in analyzing network protocol implementations). The most widely used AAL algorithms generate finite state machine models, such as Mealy machines. For many analysis tasks, however, it is crucial to generate richer classes of models that also show how relations between
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Constrained Multi-Tildes: Derived Term and Position Automata arXiv.cs.FL Pub Date : 2024-01-22 Samira Attou, Ludovic Mignot, Clément Miklarz, Florent Nicart
Multi-tildes are regular operators that were introduced to enhance the factorization power of regular expressions, allowing us to add the empty word in several factors of a catenation product of languages. In addition to multi-bars, which dually remove the empty word, they allow representing any acyclic automaton by a linear-sized expression, whereas the lower bound is exponential in the classic case
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On-The-Fly Algorithm for Reachability in Parametric Timed Games (Extended Version) arXiv.cs.FL Pub Date : 2024-01-20 Mikael Bisgaard Dahlsen-JensenAarhus University, Aarhus, Denmark, Baptiste FievetUniversité Sorbonne Paris Nord CNRS, Villetaneuse, France, Laure PetrucciUniversité Sorbonne Paris Nord CNRS, Villetaneuse, France, Jaco van de PolAarhus University, Aarhus, Denmark
Parametric Timed Games (PTG) are an extension of the model of Timed Automata. They allow for the verification and synthesis of real-time systems, reactive to their environmeand depending on adjustable parameters. Given a PTG and a reachability objective, we synthesize the values of the parameters such that the game is winning for the controller. We adapt and implement the On-The-Fly algorithm for parameter
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Verification under TSO with an infinite Data Domain arXiv.cs.FL Pub Date : 2024-01-18 Parosh Aziz Abdulla, Mohamed Faouzi Atig, Florian Furbach, Shashwat Garg
We examine verification of concurrent programs under the total store ordering (TSO) semantics used by the x86 architecture. In our model, threads manipulate variables over infinite domains and they can check whether variables are related for a range of relations. We show that, in general, the control state reachability problem is undecidable. This result is derived through a reduction from the state
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Verification and Enforcement of Strong State-Based Opacity for Discrete-Event Systems arXiv.cs.FL Pub Date : 2024-01-18 Xiaoguang Han, Kuize Zhang, Zhiwu Li
In this paper, we investigate the verification and enforcement of strong state-based opacity (SBO) in discrete-event systems modeled as partially-observed (nondeterministic) finite-state automata, including strong K-step opacity (K-SSO), strong current-state opacity (SCSO), strong initial-state opacity (SISO), and strong infinite-step opacity (Inf-SSO). They are stronger versions of four widely-studied
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Monoidal Extended Stone Duality arXiv.cs.FL Pub Date : 2024-01-16 Fabian Birkmann, Henning Urbat, Stefan Milius
Extensions of Stone-type dualities have a long history in algebraic logic and have also been instrumental for proving results in algebraic language theory. We show how to extend abstract categorical dualities via monoidal adjunctions, subsuming various incarnations of classical extended Stone and Priestley duality as a special case. Guided by these categorical foundations, we investigate residuation
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Anti-Context-Free languages arXiv.cs.FL Pub Date : 2024-01-15 Carles Cardó
Context-free languages can be characterized in several ways. This article studies projective linearisations of languages of simple dependency trees, i.e., dependency trees in which a node can govern at most one node with a given syntactic function. We prove that the projective linearisations of local languages of simple dependency trees coincide with the context-free languages. Simple dependency trees
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Directed Regular and Context-Free Languages arXiv.cs.FL Pub Date : 2024-01-13 Moses Ganardi, Irmak Saglam, Georg Zetzsche
We study the problem of deciding whether a given language is directed. A language $L$ is \emph{directed} if every pair of words in $L$ have a common (scattered) superword in $L$. Deciding directedness is a fundamental problem in connection with ideal decompositions of downward closed sets. Another motivation is that deciding whether two \emph{directed} context-free languages have the same downward
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On the Boolean Closure of Deterministic Top-Down Tree Automata arXiv.cs.FL Pub Date : 2024-01-12 Christof Löding, Wolfgang Thomas
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether it belongs to this class is open. We provide some progress by two results: First, a characterization of this class by a natural extension of deterministic top-down
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Linear-size Suffix Tries and Linear-size CDAWGs Simplified and Improved arXiv.cs.FL Pub Date : 2024-01-09 Shunsuke Inenaga
The linear-size suffix tries (LSTries) [Crochemore et al., TCS 2016] are a version of suffix trees in which the edge labels are single characters, yet are able to perform pattern matching queries in optimal time. Instead of explicitly storing the input text, LSTries have some extra non-branching internal nodes called type-2 nodes. The extended techniques are then used in the linear-size compact directed
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Classifying Words with 3-sort Automata arXiv.cs.FL Pub Date : 2024-01-02 Tomasz Jastrząb, Frédéric Lardeux, Eric Monfroy
Grammatical inference consists in learning a language or a grammar from data. In this paper, we consider a number of models for inferring a non-deterministic finite automaton (NFA) with 3 sorts of states, that must accept some words, and reject some other words from a given sample. We then propose a transformation from this 3-sort NFA into weighted-frequency and probabilistic NFA, and we apply the
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3-anti-power uniform morphisms arXiv.cs.FL Pub Date : 2023-12-22 Francis WlazinskiLAMFA
Words whose three successive factors of the same length are all different i.e. 3-anti-power words are a natural extension of square-free words (two successive factors of the same length are different). We give a way to verify whether a uniform morphism preserves 3-anti-power words (the image of a 3-anti-power word is a 3-anti-power word). A consequence of the existence of such morphisms is the possibility
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Weighted Automata and Logics Meet Computational Complexity arXiv.cs.FL Pub Date : 2023-12-17 Peter Kostolányi
Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in terms of a class $\mathbf{NP}[S]$ for a suitable semiring $S$, defined via weighted Turing machines over $S$ similarly as $\mathbf{NP}$ is defined via the classical
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Finer characterization of bounded languages described by GF(2)-grammars arXiv.cs.FL Pub Date : 2023-12-11 Vladislav Makarov, Marat Movsin
GF(2)-grammars are a somewhat recently introduced grammar family that have some unusual algebraic properties and are closely connected to unambiguous grammars. In "Bounded languages described by GF(2)-grammars", Makarov proved a necessary condition for subsets of $a_1^* a_2^* \cdots a_k^*$ to be described by some GF(2)-grammar. By extending these methods further, we prove an even stronger upper bound
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Stochastic Directly-Follows Process Discovery Using Grammatical Inference arXiv.cs.FL Pub Date : 2023-12-09 Hanan Alkhammash, Artem Polyvyanyy, Alistair Moffat
Starting with a collection of traces generated by process executions, process discovery is the task of constructing a simple model that describes the process, where simplicity is often measured in terms of model size. The challenge of process discovery is that the process of interest is unknown, and that while the input traces constitute positive examples of process executions, no negative examples
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When Input Integers are Given in the Unary Numeral Representation arXiv.cs.FL Pub Date : 2023-12-07 Tomoyuki Yamakami
Many NP-complete problems take integers as part of their input instances. These input integers are generally binarized, that is, provided in the form of the "binary" numeral representation, and the lengths of such binary forms are used as a basis unit to measure the computational complexity of the problems. In sharp contrast, the "unarization" (or the "unary" numeral representation) of numbers has
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Subsets of groups with context-free preimages arXiv.cs.FL Pub Date : 2023-12-07 Alex Levine
We study subsets $E$ of finitely generated groups where the set of all words over a given finite generating set that lie in $E$ forms a context-free language. We call these sets recognisably context-free. They are invariant of the choice of generating set and a theorem of Muller and Schupp fully classifies when the set $\{1\}$ can be recognisably context-free. We extend Muller and Schupp's result to
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A Linear-time Simulation of Deterministic $d$-Limited Automata arXiv.cs.FL Pub Date : 2023-12-04 Alexander Rubtsov
A $d$-limited automaton is a Turing machine that uses only the cells with the input word (and end-markers) and rewrites symbols only in the first $d$ visits. This model was introduced by T. Hibbard in 1967 and he showed that $d$-limited automata recognize context-free languages for each $d \geq 2$. He also proved that languages recognizable by deterministic $d$-limited automata form a hierarchy and
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Semantics of Attack-Defense Trees for Dynamic Countermeasures and a New Hierarchy of Star-free Languages arXiv.cs.FL Pub Date : 2023-12-01 Thomas Brihaye, Sophie Pinchinat, Alexandre Terefenko
We present a mathematical setting for attack-defense trees, a classic graphical model to specify attacks and countermeasures. We equip attack-defense trees with (trace) language semantics allowing to have an original dynamic interpretation of countermeasures. Interestingly, the expressiveness of attack-defense trees coincides with star-free languages, and the nested countermeasures impact the expressiveness
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Restivo Salemi property for $α$-power free languages with $α\geq 5$ and $k\geq 3$ letters arXiv.cs.FL Pub Date : 2023-12-04 Josef Rukavicka
In 2009, Shur published the following conjecture: Let $L$ be a power-free language and let $e(L)\subseteq L$ be the set of words of $L$ that can be extended to a bi-infinite word respecting the given power-freeness. If $u, v \in e(L)$ then $uwv \in e(L)$ for some word $w$. Let $L_{k,\alpha}$ denote an $\alpha$-power free language over an alphabet with $k$ letters, where $\alpha$ is a positive rational
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Linear Matching of JavaScript Regular Expressions arXiv.cs.FL Pub Date : 2023-11-29 Aurèle BarrièreEPFL, Clément Pit-ClaudelEPFL
Modern regex languages have strayed far from well-understood traditional regular expressions: they include features that fundamentally transform the matching problem. In exchange for these features, modern regex engines at times suffer from exponential complexity blowups, a frequent source of denial-of-service vulnerabilities in JavaScript applications. Worse, regex semantics differ across languages
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Traversing automata with current state uncertainty under LTL$_f$ constraints arXiv.cs.FL Pub Date : 2023-11-29 Andrew Ryzhikov, Petra Wolf
In this paper, we consider a problem which we call LTL$_f$ model checking on paths: given a DFA $\mathcal{A}$ and a formula $\phi$ in LTL on finite traces, does there exist a word $w$ such that every path starting in a state of $\mathcal{A}$ and labeled by $w$ satisfies $\phi$? The original motivation for this problem comes from the constrained parts orienting problem, introduced in [Petra Wolf, "Synchronization
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A Direct Lazy Sampling Proof Technique in Probabilistic Relational Hoare Logic arXiv.cs.FL Pub Date : 2023-11-28 Roberto Metere, Changyu Dong
Programs using random values can either make all choices in advance (eagerly) or sample as needed (lazily). In formal proofs, we focus on indistinguishability between two lazy programs, a common requirement in the random oracle model (ROM). While rearranging sampling instructions often solves this, it gets complex when sampling is spread across procedures. The traditional approach, introduced by Bellare
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The Complexity of Second-order HyperLTL arXiv.cs.FL Pub Date : 2023-11-27 Martin Zimmermann
We determine the complexity of second-order HyperLTL satisfiability and model-checking: Both are as hard as truth in third-order arithmetic.
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Random generation of group elements using combinatorial group theory and automata theory, along with a hardware example arXiv.cs.FL Pub Date : 2023-11-27 MohammadJavad Vaez, Marjan Kaedi, Mahdi Kalbasi
In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we explore the application of this method in generating random elements of a particularly significant group, namely the symmetric group (or group of permutations on
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Concurrent Stochastic Lossy Channel Games arXiv.cs.FL Pub Date : 2023-11-28 Daniel Stan, Muhammad Najib, Anthony Widjaja Lin, Parosh Aziz Abdulla
Concurrent stochastic games are an important formalism for the rational verification of probabilistic multi-agent systems, which involves verifying whether a temporal logic property is satisfied in some or all game-theoretic equilibria of such systems. In this work, we study the rational verification of probabilistic multi-agent systems where agents can cooperate by communicating over unbounded lossy
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Extending the WMSO+U Logic With Quantification Over Tuples arXiv.cs.FL Pub Date : 2023-11-28 Anita Badyl, Paweł Parys
We study a new extension of the weak MSO logic, talking about boundedness. Instead of a previously considered quantifier U, expressing the fact that there exist arbitrarily large finite sets satisfying a given property, we consider a generalized quantifier U, expressing the fact that there exist tuples of arbitrarily large finite sets satisfying a given property. First, we prove that the new logic
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An Exploration of Left-Corner Transformations arXiv.cs.FL Pub Date : 2023-11-27 Andreas Opedal, Eleftheria Tsipidi, Tiago Pimentel, Ryan Cotterell, Tim Vieira
The left-corner transformation (Rosenkrantz and Lewis, 1970) is used to remove left recursion from context-free grammars, which is an important step towards making the grammar parsable top-down with simple techniques. This paper generalizes prior left-corner transformations to support semiring-weighted production rules and to provide finer-grained control over which left corners may be moved. Our generalized
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On the piecewise complexity of words and periodic words arXiv.cs.FL Pub Date : 2023-11-26 M. Praveen, Philippe Schnoebelen, Isa Vialard, Julien Veron
The piecewise complexity $h(u)$ of a word is the minimal length of subwords needed to exactly characterise $u$. Its piecewise minimality index $\rho(u)$ is the smallest length $k$ such that $u$ is minimal among its order-$k$ class $[u]_k$ in Simon's congruence. We study these two measures and provide efficient algorithms for computing $h(u)$ and $\rho(u)$. We also provide efficient algorithms for the
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On universality of regular realizability problems arXiv.cs.FL Pub Date : 2023-11-26 Alexander Rubtsov, Michael Vyalyi
We prove universality of the regular realizability problems for several classes of filters. The filters are descriptions of finite relations on the set of non-negative integers in the format proposed by P. Wolf and H. Fernau. The universality has proven up to reductions using NP-oracles. It corresponds to the results of P. Wolf and H. Fernau about decidability of regular realizability problems for
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Careful Synchronization of One-Cluster Automata arXiv.cs.FL Pub Date : 2023-11-25 Jakub Ruszil
In this paper we investigate careful synchronization of one-cluster partial automata. First we prove that in general case the shortest carefully synchronizing word for such automata is of length $2^\frac{n}{2} + 1$, where $n$ is the number of states of an automaton. Additionally we prove that checking whether a given one-cluster partial automaton is carefully synchronizing is NP-hard even in the case
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Repetition factorization of automatic sequences arXiv.cs.FL Pub Date : 2023-11-25 Jeffrey Shallit, Xinhao Xu
Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several (generalized) automatic sequences, including the infinite Fibonacci word, the Thue-Morse word, paperfolding words, and the Rudin-Shapiro sequence.
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Characterising and Verifying the Core in Concurrent Multi-Player Mean-Payoff Games (Full Version) arXiv.cs.FL Pub Date : 2023-11-27 Julian Gutierrez, Anthony W. Lin, Muhammad Najib, Thomas Steeples, Michael Wooldridge
Concurrent multi-player mean-payoff games are important models for systems of agents with individual, non-dichotomous preferences. Whilst these games have been extensively studied in terms of their equilibria in non-cooperative settings, this paper explores an alternative solution concept: the core from cooperative game theory. This concept is particularly relevant for cooperative AI systems, as it
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Simulation Limitations of Affine Cellular Automata arXiv.cs.FL Pub Date : 2023-11-24 Barbora Hudcová, Jakub Krásenský
Cellular automata are a famous model of computation, yet it is still a challenging task to assess the computational capacity of a given automaton; especially when it comes to showing negative results. In this paper, we focus on studying this problem via the notion of CA relative simulation. We say that automaton A is simulated by B if each space-time diagram of A can be, after suitable transformations
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The analogue of overlap-freeness for the Fibonacci morphism arXiv.cs.FL Pub Date : 2023-11-21 James D. Currie, Narad Rampersad
A $4^-$-power is a non-empty word of the form $XXXX^-$, where $X^-$ is obtained from $X$ by erasing the last letter. A binary word is called {\em faux-bonacci} if it contains no $4^-$-powers, and no factor 11. We show that faux-bonacci words bear the same relationship to the Fibonacci morphism that overlap-free words bear to the Thue-Morse morphism. We prove the analogue of Fife's Theorem for faux-bonacci