显示样式： 排序： IF:  GO 导出

Quantum algorithm for Dyck Language with Multiple Types of Brackets arXiv.cs.FL Pub Date : 20210617
Kamil Khadiev, Dmitry KravchenkoWe consider the recognition problem of the Dyck Language generalized for multiple types of brackets. We provide an algorithm with quantum query complexity $O(\sqrt{n}(\log n)^{0.5k})$, where $n$ is the length of input and $k$ is the maximal nesting depth of brackets. Additionally, we show the lower bound for this problem which is $O(\sqrt{n}c^{k})$ for some constant $c$. Interestingly, classical algorithms

The Connection between Process Complexity of Event Sequences and Models discovered by Process Mining arXiv.cs.FL Pub Date : 20210615
Adriano Augusto, Jan Mendling, Maxim Vidgof, Bastian WurmProcess mining is a research area focusing on the design of algorithms that can automatically provide insights into business processes by analysing historic process execution data, known as event logs. Among the most popular algorithms are those for automated process discovery, whose ultimate goal is to generate the best process model that summarizes the behaviour recorded in the input event log. Over

On Star Expressions and Coalgebraic Completeness Theorems arXiv.cs.FL Pub Date : 20210615
Todd Schmid, Jurriaan Rot, Alexandra SilvaAn open problem posed by Milner asks for a proof that a certain axiomatisation, which Milner showed is sound with respect to bisimilarity for regular expressions, is also complete. One of the main difficulties of the problem is the lack of a full Kleene theorem, since there are automata that can not be specified, up to bisimilarity, by an expression. Grabmayer and Fokkink (2020) characterise those

Hip to Be (Latin) Square: Maximal Period Sequences from Orthogonal Cellular Automata arXiv.cs.FL Pub Date : 20210614
Luca MariotOrthogonal Cellular Automata (OCA) have been recently investigated in the literature as a new approach to construct orthogonal Latin squares for cryptographic applications such as secret sharing schemes. In this paper, we consider OCA for a different cryptographic task, namely the generation of pseudorandom sequences. The idea is to iterate a dynamical system where the output of an OCA pair is fed

Automatic winning shifts arXiv.cs.FL Pub Date : 20210614
Jarkko Peltomäki, Ville SaloTo each onedimensional subshift $X$, we may associate a winning shift $W(X)$ which arises from a combinatorial game played on the language of $X$. Previously it has been studied what properties of $X$ does $W(X)$ inherit. For example, $X$ and $W(X)$ have the same factor complexity and if $X$ is a sofic subshift, then $W(X)$ is also sofic. In this paper, we develop a notion of automaticity for $W(X)$

Minimality Notions via Factorization Systems arXiv.cs.FL Pub Date : 20210614
Thorsten WißmannFor the minimization of statebased systems (i.e. the reduction of the number of states while retaining the system's semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the system. In the present article, we relate the two aspects on coalgebras by defining an abstract notion of minimality using factorization systems. We will find criteria

Minimization and Canonization of GFG TransitionBased Automata arXiv.cs.FL Pub Date : 20210612
Bader Abu Radi, Orna KupfermanWhile many applications of automata in formal methods can use nondeterministic automata, some applications, most notably synthesis, need deterministic or goodforgames(GFG) automata. The latter are nondeterministic automata that can resolve their nondeterministic choices in a way that only depends on the past. The minimization problem for deterministic B\"uchi and coB\"uchi word automata is NPcomplete

Matching Patterns with Variables under Hamming Distance arXiv.cs.FL Pub Date : 20210611
Paweł Gawrychowski, Florin Manea, Stefan SiemerA pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching problem, i.e., deciding whether a given pattern matches a given word, was heavily investigated: it is NPcomplete in general, but can be solved efficiently for classes

Generalized Circular OneWay Jumping Finite Automata arXiv.cs.FL Pub Date : 20210605
Ujjwal Kumar Mishra, Kalpana Mahalingam, Rama RaghavanA discontinuous model of computation called oneway jumping finite automata was defined by H. Chigahara et. al. This model was a restricted version of the model jumping finite automata. Oneway jumping finite automata change their states after deleting a letter of an input and jump only in one direction. Allowing a state to delete a subword instead of a letter, we define a new model generalized circular

Reduction Using Induced Subnets To Systematically Prove Properties For FreeChoice Nets arXiv.cs.FL Pub Date : 20210607
Wil M. P. van der AalstWe use sequences of tinduced Tnets and pinduced Pnets to convert freechoice nets into Tnets and Pnets while preserving properties such as wellformedness, liveness, lucency, pcsafety, and perpetuality. The approach is general and can be applied to different properties. This allows for more systematic proofs that "peel off" nontrivial parts while retaining the essence of the problem (e.g.,

FreeChoice Nets With Home Clusters Are Lucent arXiv.cs.FL Pub Date : 20210607
Wil M. P. van der AalstA marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. Characterizing the class of systems that are lucent is a foundational and also challenging question. However, little research has been done on the topic. In this paper, it is shown that all freechoice nets having a

Generalized Linear OneWay Jumping Finite Automata arXiv.cs.FL Pub Date : 20210605
Ujjwal Kumar Mishra, Kalpana Mahalingam, Rama RaghavanA new discontinuous model of computation called oneway jumping finite automata was defined by H. Chigahara et. al. This model was a restricted version of the model jumping finite automata. These automata read an input symbolbysymbol and jump only in one direction. A generalized linear oneway jumping finite automaton makes jumps after deleting a substring of an input string and then changes its

Detecting plainness in PSPACE arXiv.cs.FL Pub Date : 20210607
Murray Elder, Adam PiggottWe show that groups presented by inverseclosed finite convergent lengthreducing rewriting systems are characterised by a striking geometric property: nondegenerate triangles in their Cayley graph have uniformly bounded size. We then define a simple relation on the set of nontrivial finiteorder elements of the group, and prove that the group is plain if and only if this relation is transitive on

Verification in the Loop: CorrectbyConstruction Control Learning with Reachavoid Guarantees arXiv.cs.FL Pub Date : 20210606
Yixuan Wang, Chao Huang, Zhaoran Wang, Zhilu Wang, Qi ZhuIn the current control design of safetycritical autonomous systems, formal verification techniques are typically applied after the controller is designed to evaluate whether the required properties (e.g., safety) are satisfied. However, due to the increasing system complexity and the fundamental hardness of designing a controller with formal guarantees, such an openloop process of designthenverify

Closed ZivLempel factorization of the $m$bonacci words arXiv.cs.FL Pub Date : 20210606
Marieh Jahannia, Morteza Mohammadnoori, Narad Rampersad, Manon StipulantiA word $w$ is said to be closed if it has a proper factor $x$ which occurs exactly twice in $w$, as a prefix and as a suffix of $w$. Based on the concept of ZivLempel factorization, we define the closed $z$factorization of finite and infinite words. Then we find the closed $z$factorization of the infinite $m$bonacci words for all $m \geq 2$. We also classify closed prefixes of the infinite $m$bonacci

Extracting Weighted Automata for Approximate Minimization in Language Modelling arXiv.cs.FL Pub Date : 20210605
Clara Lacroce, Prakash Panangaden, Guillaume RabusseauIn this paper we study the approximate minimization problem for language modelling. We assume we are given some language model as a black box. The objective is to obtain a weighted finite automaton (WFA) that fits within a given size constraint and which mimics the behaviour of the original model while minimizing some notion of distance between the black box and the extracted WFA. We provide an algorithm

The Inclusion Problem for Forest Languages under Substitutions arXiv.cs.FL Pub Date : 20210604
Marcial Gaißert, Manfred KufleitnerWe consider algorithms and lower bounds for various problems over forest languages; as input models we allow forest algebras, deterministic forest automata and nondeterministic forest automata. For the equivalence problem, we give an almostlineartime algorithm for both forest algebras and deterministic forest automata; this is complemented by a polynomial time hardness result. The emptiness problem

Verification Tools for Checking some kinds of Testability arXiv.cs.FL Pub Date : 20210604
A. N. TrahtmanA locally testable language L is a language with the property that for some non negative integer k, called the order of local testability, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k + 1 and (2) the set of intermediate substrings of length k of the word u. For given k the language is called ktestable. The local testability has a wide

On (colex) Ordering Automata arXiv.cs.FL Pub Date : 20210604
Giovanna D'Agostino, Nicola Cotumaccio, Alberto Policriti, Nicola PrezzaThe states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A))  the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible orders a very natural one is the colexicographic one. Such naturalness stems from the fact that it suggests a transfer of the order from words to the automaton's

Maximizing Extractable Value from Automated Market Makers arXiv.cs.FL Pub Date : 20210602
Massimo Bartoletti, James Hsinyu Chiang, Alberto LluchLafuenteAutomated Market Makers (AMMs) are decentralized applications that allow users to exchange cryptotokens without the need to find a matching exchange order. AMMs are one of the most successful DeFi use case so far, as the main AMM platforms UniSwap and Balancer process a daily volume of transactions worth billions of dollars. Despite this success story, AMMs are wellknown to suffer from transactionordering

Hilbert's spacefilling curve described by automatic, regular, and synchronized sequences arXiv.cs.FL Pub Date : 20210602
Jeffrey ShallitWe describe Hilbert's spacefilling curve in several different ways: as an automatic sequence of directions,as a regular and synchronized sequence of coordinates of lattice points encountered, and as an automatic bitmap image.

Ordering regular languages: a danger zone arXiv.cs.FL Pub Date : 20210601
Giovanna D'Agostino, Davide Martincigh, Alberto PolicritiOrdering the collection of states of a given automaton starting from an order of the underlying alphabet is a natural move towards a computational treatment of the language accepted by the automaton. Along this path, Wheeler \emph{graphs} have been recently introduced as an extension/adaptation of the BurrowsWheeler Transform (the now famous BWT, originally defined on strings) to graphs. These graphs

Detecting a single fault in a deterministic finite automaton arXiv.cs.FL Pub Date : 20210601
Artur Polański, Eryk LipkaGiven a deterministic finite automaton and its implementation with at most one single fault, that we can test on a set of inputs, we provide an algorithm to find a test set that guarantees finding whether the fault exists.

A Grammatical Approach for Distributed Business Process Management using Structured and Cooperatively Edited Mobile Artifacts arXiv.cs.FL Pub Date : 20210531
Milliam Maxime Zekeng NdadjiIn this thesis, we focus on the proposal of distributed workflow systems dedicated to the automation of administrative business processes. We propose an approach to build such systems by relying on the concepts of multiagent systems, Peer to Peer (P2P) architecture, ServiceOriented Architecture (SOA) and structured documents (artifacts) cooperative edition. Indeed, we develop mathematical tools that

A new distance based on minimal absent words and applications to biological sequences arXiv.cs.FL Pub Date : 20210531
Giuseppa Castiglione, Jia Gao, Sabrina Mantaci, Antonio RestivoA minimal absent word of a sequence x, is a sequence yt hat is not a factorof x, but all of its proper factors are factors of x as well. The set of minimal absent words uniquely defines the sequence itself. In recent times minimal absent words have been used in order to compare sequences. In fact, to do this, one can compare the sets of their minimal absent words. Chairungasee and Crochemorein [2]

Lower Bounds for the Number of Repetitions in 2D Strings arXiv.cs.FL Pub Date : 20210531
Paweł Gawrychowski, Samah Ghazawi, Gad M. LandauA twodimensional string is simply a twodimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs. First, we construct an infinite family of $n\times n$ 2D strings with $\Omega(n^{3})$ distinct tandems. Second, we construct an infinite family of $n\times n$ 2D

Definability Results for TopDown Tree Transducers arXiv.cs.FL Pub Date : 20210531
Sebastian Maneth, Helmut Seidl, Martin VuWe prove that for a given deterministic topdown transducer with lookahead it is decidable whether or not its translation is definable (1)~by a linear topdown tree transducer or (2)~by a tree homomorphism. We present algorithms that construct equivalent such transducers if they exist.

Emergence and algorithmic information dynamics of systems and observers arXiv.cs.FL Pub Date : 20210531
Felipe S. Abrahão, Hector ZenilPrevious work has shown that perturbation analysis in algorithmic information dynamics can uncover generative causal processes of finite objects and quantify each of its element's information contribution to computably constructing the objects. One of the challenges for defining emergence is that the dependency on the observer's previous knowledge may cause a phenomenon to present itself as emergent

A Rice's Theorem for Abstract Semantics arXiv.cs.FL Pub Date : 20210530
Paolo Baldan, Francesco Ranzato, Linpeng ZhangClassical results in computability theory, notably Rice's theorem, focus on the extensional content of programs, namely, on the partial recursive functions that programs compute. Later and more recent work investigated intensional generalisations of such results that take into account the way in which functions are computed, thus affected by the specific programs computing them. In this paper, we single

Adapting Behaviors via Reactive Synthesis arXiv.cs.FL Pub Date : 20210528
Gal Amram, Suguman Bansal, Dror Fried, Lucas M. Tabajara, Moshe Y. Vardi, Gera WeissIn the \emph{Adapter Design Pattern}, a programmer implements a \emph{Target} interface by constructing an \emph{Adapter} that accesses an existing \emph{Adaptee} code. In this work, we present a reactive synthesis interpretation to the adapter design pattern, wherein an algorithm takes an \emph{Adaptee} and a \emph{Target} transducers, and the aim is to synthesize an \emph{Adapter} transducer that

Fast zonebased algorithms for reachability in pushdown timed automata arXiv.cs.FL Pub Date : 20210528
S. Akshay, Paul Gastin, Karthik R PrakashGiven the versatility of timed automata a huge body of work has evolved that considers extensions of timed automata. One extension that has received a lot of interest is timed automata with a, possibly unbounded, stack, also called the pushdown timed automata (PDTA) model. While different algorithms have been given for reachability in different variants of this model, most of these results are purely

A package TESTAS for checking some kinds of testability arXiv.cs.FL Pub Date : 20210526
A. N. TrahtmanWe implement a set of procedures for deciding whether or not a language given by its minimal automaton or by its syntactic semigroup is locally testable, right or left locally testable, threshold locally testable, strictly locally testable, or piecewise testable. The bounds on order of local testability of transition graph and order of local testability of transition semigroup are also found. For given

An explicit algorithm for normal forms in small overlap monoids arXiv.cs.FL Pub Date : 20210525
James D. Mitchell, Maria TsalakouIf $\mathcal{P} = \left\langle A \,  \,R \right\rangle$ is a monoid presentation, then the relation words in $\mathcal{P}$ are just the set of words on the left or right hand side of any pair in $R$. A word $w\in A ^*$ is said to be a piece of $\mathcal{P}$ if $w$ is a factor of at least two distinct relation words, or $w$ occurs more than once as a factor of a single relation word (possibly overlapping)

The Pseudofinite Monadic Second Order Theory of Linear Order arXiv.cs.FL Pub Date : 20210525
Deacon LinkhornMonadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of linear order, using a first order setup . We give explicit (and recursive) axioms and characterise the completions in terms of residue sequences. A connection with profinite

On the Minimisation of TransitionBased Rabin Automata and the Chromatic Memory Requirements of Muller Conditions arXiv.cs.FL Pub Date : 20210525
Antonio CasaresIn this paper, we prove the NPcompleteness of the minimisation of transitionbased Rabin automata. We also show that the minimal amount of memory required to solve games using a given Muller condition is exactly the size of a minimal Rabin automaton recognising this condition, if we only allow chromatic memories. We deduce that finding the chromatic memory requirements of a Muller condition is NPcomplete

Automata Learning for Automated Test Generation of Real Time Localization Systems arXiv.cs.FL Pub Date : 20210521
Swantje Plambeck, Jakob Schyga, Johannes Hinckeldeyn, Jochen Kreutzfeldt, Görschwin FeyCyber Physical Systems (CPSs) are often black box systems for which no exact model exists. Automata learning allows to build abstract models of CPSs and is used in several scenarios, i.e. simulation, monitoring, and test case generation. Real time localization systems (RTLSs) are an example of particularly complex and often safety critical CPSs. We present a procedure for automatic test case generation

A numeration system for Fibonaccilike Wang shifts arXiv.cs.FL Pub Date : 20210525
Sébastien Labbé, Jana LepšováMotivated by the study of Fibonaccilike Wang shifts, we define a numeration system for $\mathbb{Z}$ and $\mathbb{Z}^2$ based on the binary alphabet $\{0,1\}$. We introduce a set of 16 Wang tiles that admits a valid tiling of the plane described by a deterministic finite automaton taking as input the representation of a position $(m,n)\in\mathbb{Z}^2$ and outputting a Wang tile.

Inferring Temporal Logic Properties from Data using Boosted Decision Trees arXiv.cs.FL Pub Date : 20210524
Erfan Aasi, Cristian Ioan Vasile, Mahroo Bahreinian, Calin BeltaMany autonomous systems, such as robots and selfdriving cars, involve realtime decision making in complex environments, and require prediction of future outcomes from limited data. Moreover, their decisions are increasingly required to be interpretable to humans for safe and trustworthy coexistence. This paper is a first step towards interpretable learningbased robot control. We introduce a novel

Asynchronous wreath product and cascade decompositions for concurrent behaviours arXiv.cs.FL Pub Date : 20210523
Bharat Adsul, Paul Gastin, Saptarshi Sarkar, Pascal WeilWe develop new algebraic tools to reason about concurrent behaviours modelled as languages of Mazurkiewicz traces and asynchronous automata. These tools reflect the distributed nature of traces and the underlying causality and concurrency between events, and can be said to support true concurrency. They generalize the tools that have been so efficient in understanding, classifying and reasoning about

An algorithm to verify local threshold testability of deterministic finite automata arXiv.cs.FL Pub Date : 20210522
A. N. TrahtmanA locally threshold testable language L is a language with the property that for some non negative integers k and l, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k > 1 and (2) the set of intermediate substrings of length k of the word u where the sets of substrings occurring at least j times are the same, for j <= L. For given k and L the

SelfAttention Networks Can Process Bounded Hierarchical Languages arXiv.cs.FL Pub Date : 20210524
Shunyu Yao, Binghui Peng, Christos Papadimitriou, Karthik NarasimhanDespite their impressive performance in NLP, selfattention networks were recently proved to be limited for processing formal languages with hierarchical structure, such as $\mathsf{Dyck}_k$, the language consisting of wellnested parentheses of $k$ types. This suggested that natural language can be approximated well with models that are too weak for formal languages, or that the role of hierarchy

Runtime Enforcement of Programmable Logic Controllers arXiv.cs.FL Pub Date : 20210522
Ruggero Lanotte, Massimo Merro, Andrei MunteanuWith the advent of Industry 4.0, industrial facilities and critical infrastructures are transforming into an ecosystem of heterogeneous physical and cyber components, such as programmable logic controllers, increasingly interconnected and therefore exposed to cyberphysical attacks, i.e., security breaches in cyberspace that may adversely affect the physical processes underlying industrial control

Minimization and Synthesis of the Tail inSequential Compositions of Mealy Machines arXiv.cs.FL Pub Date : 20210521
Alberto Larrauri, Roderick BloemWe consider a system consisting of a sequential composition of Mealy machines, called head and tail. We study two problems related to these systems. First, models of both head and tail components are available, and the aim is to obtain a replacement for the tail with the minimum number of states. We introduce a minimization method for this context which yields an exponential improvement over the state

Decision Questions for Probabilistic Automata on Small Alphabets arXiv.cs.FL Pub Date : 20210521
Paul C. Bell, Pavel SemukhinWe study the emptiness and $\lambda$reachability problems for unary and binary Probabilistic Finite Automata (PFA) and characterise the complexity of these problems in terms of the degree of ambiguity of the automaton and the size of its alphabet. Our main result is that emptiness and $\lambda$reachability are solvable in EXPTIME for polynomially ambiguous unary PFA and if, in addition, the transition

Transducer Synthesis from Universal Register Automata in (N,>) arXiv.cs.FL Pub Date : 20210520
Ayrat Khalimov, Emmanuel Filiot, Léo ExibardThis paper concerns the problem of reactive synthesis of systems interacting with its environment via letters from an infinite data domain. Register automata and transducers are popular formalisms for specifying and modeling such systems. They extend finitestate automata by introducing registers that are used to store data and to test incoming data against the stored one. Unlike the standard automata

Forest languages defined by counting maximal paths arXiv.cs.FL Pub Date : 20210520
Martin BeaudryA leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaftoroot paths make up a word that belongs to $L$. We look at the class $\mathsf{*D}$ of the languages recognized by iterated wreath products of syntactic algebras of leaf path languages. We prove

Conelikes and Ranker Comparisons arXiv.cs.FL Pub Date : 20210519
Viktor Henriksson, Manfred KufleitnerFor every fixed class of regular languages, there is a natural hierarchy of increasingly more general problems: Firstly, the membership problem asks whether a given language belongs to the fixed class of languages. Secondly, the separation problem asks for two given languages whether they can be separated by a language from the fixed class. And thirdly, the covering problem is a generalization of separation

An Algebraic Characterisation of FirstOrder Logic with Neighbour arXiv.cs.FL Pub Date : 20210519
Amaldev Manuel, Dhruv NevatiaWe give an algebraic characterisation of firstorder logic with the neighbour relation, on finite words. For this, we consider languages of finite words over alphabets with an involution on them. The natural algebras for such languages are involution semigroups. To characterise the logic, we define a special kind of semidirect product of involution semigroups, called the locally hermitian product.

Deciding FO2 Alternation for Automata over Finite and Infinite Words arXiv.cs.FL Pub Date : 20210519
Viktor Henriksson, Manfred KufleitnerWe consider twovariable firstorder logic $\text{FO}^2$ and its quantifier alternation hierarchies over both finite and infinite words. Our main results are forbidden patterns for deterministic automata (finite words) and for CartonMichel automata (infinite words). In order to give concise patterns, we allow the use of subwords on paths in finite graphs. This concept is formalized as subword patterns

The Černy Conjecture for aperiodic automata arXiv.cs.FL Pub Date : 20210519
A. N. TrahtmanA word w is called a synchronizing (recurrent, reset) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some state; a DFA that has a synchronizing word is said to be synchronizing. Cerny conjectured in 1964 that every nstate synchronizing DFA possesses a synchronizing word of length at most (n 1)2. We consider automaton with aperiodic transition monoid (such

Wilf classes of nonsymmetric operads arXiv.cs.FL Pub Date : 20210519
Andrey T. Cherkasov, Dmitri PiontkovskiTwo operads are said to belong to the same Wilf class if they have the same generating series. We discuss possible Wilf classifications of nonsymmetric operads with monomial relations. As a corollary, this would give the same classification for the operads with a finite Groebner basis. Generally, there is no algorithm to decide whether two finitely presented operads belong to the same Wilf class.

Improved Ackermannian lower bound for the VASS reachability problem arXiv.cs.FL Pub Date : 20210518
Sławomir LasotaThis draft is a followup of the Ackermannian lower bound for the reachability problem in vector addition systems with states (VASS), recently announced by Czerwi\'nski and Orlikowski. Independently, the same result has been announced by Leroux, but with a significantly different proof. We provide a simplification of the former construction, thus improving the lower bound for VASS in fixed dimension:

Comparisonfree polyregular functions arXiv.cs.FL Pub Date : 20210518
Lê Thành Dũng NguyênUP13, Camille Noûs, Pierre PradicWe study automatatheoretic classes of stringtostring functions whose output may grow faster than linearly in their input. Our central contribution is to introduce a new such class, with polynomial growth and three equivalent definitions: the smallest class containing regular functions and closed under a "composition by substitution" operation; a restricted variant of pebble transducers; a $\lambda$calculus

Combinatorics of minimal absent words for a sliding window arXiv.cs.FL Pub Date : 20210518
Tooru Akagi, Yuki Kuhara, Takuya Mieno, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki TakedaA string $w$ is called a minimal absent word (MAW) for another string $T$ if $w$ does not occur in $T$ but the proper substrings of $w$ occur in $T$. For example, let $\Sigma = \{\mathtt{a, b, c}\}$ be the alphabet. Then, the set of MAWs for string $w = \mathtt{abaab}$ is $\{\mathtt{aaa, aaba, bab, bb, c}\}$. In this paper, we study combinatorial properties of MAWs in the sliding window model, namely

On Complementing Unambiguous Automata and Graphs With Many Cliques and Cocliques arXiv.cs.FL Pub Date : 20210516
Emil Indzhev, Stefan KieferWe show that for any unambiguous finite automaton with $n$ states there exists an unambiguous finite automaton with $\sqrt{n+1} \cdot 2^{n/2}$ states that recognizes the complement language. This builds and improves upon a similar result by Jir\'asek et al. [Int. J. Found. Comput. Sci. 29 (5) (2018)]. Our improvement is based on a reduction to and an analysis of a problem from extremal graph theory:

Leveraging Classification Metrics for Quantitative SystemLevel Analysis with Temporal Logic Specifications arXiv.cs.FL Pub Date : 20210516
Apurva Badithela, Tichakorn Wongpiromsarn, Richard M. MurrayIn many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multiclass classification. We define the probability of satisfaction of a linear temporal logic

Sofically presented dynamical systems arXiv.cs.FL Pub Date : 20210514
Johan Kopra, Ville SaloSystems obtained by quotienting a subshift of finite type (SFT) by another SFT are called finitely presented in the literature. Analogously, if a sofic shift is quotiented by a sofic equivalence relation, we call the resulting system sofically presented. Generalizing an observation of Fried, for all discrete countable monoids M, we show that Msubshift/SFT systems are precisely the expansive dynamical

Bounded Reachability Problems are Decidable in FIFO Machines arXiv.cs.FL Pub Date : 20210514
Benedikt Bollig, Alain Finkel, Amrita SureshThe undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is wellknown. In this paper, we provide an underapproximation for the general model by considering only runs that are inputbounded (i.e.\ the sequence of messages sent through a particular channel belongs to a given bounded language). We prove, by reducing this model to a counter machine

Time Flies When Looking out of the Window: Timed Games with Window Parity Objectives arXiv.cs.FL Pub Date : 20210514
James C. A. Main, Mickael Randour, Jeremy SprostonThe window mechanism was introduced by Chatterjee et al. to reinforce meanpayoff and totalpayoff objectives with time bounds in twoplayer turnbased games on graphs. It has since proved useful in a variety of settings, including parity objectives in games and both meanpayoff and parity objectives in Markov decision processes. We study window parity objectives in timed automata and timed games:

Deciding FOdefinability of Regular Languages arXiv.cs.FL Pub Date : 20210513
Agi Kurucz, Vladislav Ryzhikov, Yury Savateev, Michael ZakharyaschevWe prove that, similarly to known PSpacecompleteness of recognising FO(<)definability of the language L(A) of a DFA A, deciding both FO(<,C) and FO(<,MOD)definability are PSpacecomplete. (Here, FO(<,C) extends the firstorder logic FO(<) with the standard congruence modulo n relation, and FO(<,MOD) with the quantifiers checking whether the number of positions satisfying a given formula is divisible