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  • Binary intersection formalized
    arXiv.cs.FL Pub Date : 2020-06-30
    Štěpán Holub; Štěpán Starosta

    We provide a reformulation and a formalization of the classical result by Juhani Karhum\"aki characterizing intersections of two languages of the form $\{x,y\}^*\cap \{u,v\}^*$. We use the terminology of morphisms which allows to formulate the result in a shorter and more transparent way, and we formalize the result in the proof assistant Isabelle/HOL.

    更新日期:2020-07-01
  • Pebble Minimization of Polyregular Functions
    arXiv.cs.FL Pub Date : 2020-06-30
    Nathan Lhote

    We show that a polyregular word-to-word function is regular if and only if its output size is at most linear in its input size. Moreover a polyregular function can be realized by: a transducer with two pebbles if and only if its output has quadratic size in its input, a transducer with three pebbles if and only if its output has cubic size in its input, etc. Moreover the characterization is decidable

    更新日期:2020-07-01
  • Making Streett Determinization Tight
    arXiv.cs.FL Pub Date : 2020-06-30
    Cong Tian; Wensheng Wang; Zhenhua Duan

    Optimal determinization construction of Streett automata is an important research problem because it is indispensable in numerous applications such as decision problems for tree temporal logics, logic games and system synthesis. This paper presents a transformation from nondeterministic Streett automata (NSA) with $n$ states and $k$ Streett pairs to equivalent deterministic Rabin transition automata

    更新日期:2020-07-01
  • State Complexity of Permutation on Finite Languages
    arXiv.cs.FL Pub Date : 2020-06-26
    Stefan Hoffmann

    We investigate the state complexity of the permutation operation on finite languages. We give a tight bound that is expressed in terms of the longest strings in the unary projection languages. Moreover, we ask how large a minimal automaton could be for a finite language such that the lengths of the strings in the unary projection languages are bounded. Lastly, we look at a restricted class of languages

    更新日期:2020-06-30
  • Concept and the implementation of a tool to convert industry 4.0 environments modeled as FSM to an OpenAI Gym wrapper
    arXiv.cs.FL Pub Date : 2020-06-29
    Kallil M. C. Zielinski; Marcelo Teixeira; Richardson Ribeiro; Dalcimar Casanova

    Industry 4.0 systems have a high demand for optimization in their tasks, whether to minimize cost, maximize production, or even synchronize their actuators to finish or speed up the manufacture of a product. Those challenges make industrial environments a suitable scenario to apply all modern reinforcement learning (RL) concepts. The main difficulty, however, is the lack of that industrial environments

    更新日期:2020-06-30
  • Dissecting Power of a Finite Intersection of Deterministic Context Free Languages
    arXiv.cs.FL Pub Date : 2020-06-26
    Josef Rukavicka

    Let $\exp^{k,\alpha}$ denote a tetration function defined as follows: $\exp^{1,\alpha}=2^{\alpha}$ and $\exp^{k+1,\alpha}=2^{\exp^{k,\alpha}}$, where $k,\alpha$ are positive integers. Let $\Delta_n$ denote an alphabet with $n$ letters. If $L\subseteq\Delta_n^*$ is an infinite language such that for each $u\in L$ there is $v\in L$ with $\vert v\vert\leq \exp^{k,\alpha}\vert u\vert$ then we call $L$

    更新日期:2020-06-30
  • Detectability of labeled weighted (max-plus) automata
    arXiv.cs.FL Pub Date : 2020-06-25
    Kuize Zhang

    Discrete-event systems (DESs) are generally composed of transitions between discrete states caused by spontaneous occurrences of partially-observed events. Detectability is a fundamental property in partially-observed dynamical systems, which describes whether one can use several observed output sequences to determine the internal states of a system. In this paper, we extend results on four fundamental

    更新日期:2020-06-26
  • On morphisms preserving palindromic richness
    arXiv.cs.FL Pub Date : 2020-06-22
    Francesco Dolce; Edita Pelantová

    Droubay, Justin and Pirillo that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite "rich word" is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite words. Sturmian words and Rote complementary symmetric sequences form two classes of binary rich words, while episturmian words and words coding $d$-interval

    更新日期:2020-06-23
  • Constant-Space, Constant-Randomness Verifiers with Arbitrarily Small Error
    arXiv.cs.FL Pub Date : 2020-06-22
    M. Utkan Gezer; A. C. Cem Say

    We study the capabilities of probabilistic finite-state machines that act as verifiers for certificates of language membership for input strings, in the regime where the verifiers are restricted to toss some fixed nonzero number of coins regardless of the input size. Say and Yakary{\i}lmaz showed that the class of languages that could be verified by these machines within an error bound strictly less

    更新日期:2020-06-23
  • Rational subsets of Baumslag-Solitar groups
    arXiv.cs.FL Pub Date : 2020-06-21
    Michaël Cadilhac; Dmitry Chistikov; Georg Zetzsche

    We consider the rational subset membership problem for Baumslag-Solitar groups. These groups form a prominent class in the area of algorithmic group theory, and they were recently identified as an obstacle for understanding the rational subsets of $\text{GL}(2,\mathbb{Q})$. We show that rational subset membership for Baumslag-Solitar groups $\text{BS}(1,q)$ with $q\ge 2$ is decidable and PSPACE-complete

    更新日期:2020-06-23
  • A Fractional $3n+1$ Conjecture
    arXiv.cs.FL Pub Date : 2020-06-20
    Éric Brier; Rémi Géraud-Stewart; David Naccache

    In this paper we introduce and discuss the sequence of \emph{real numbers} defined as $u_0 \in \mathbb R$ and $u_{n+1} = \Delta(u_n)$ where \begin{equation*} \Delta(x) = \begin{cases} \frac{x}{2} &\text{if } \operatorname{frac}(x)<\frac{1}{2} \\[4px] \frac{3x+1}{2} & \text{if } \operatorname{frac}(x)\geq\frac{1}{2} \end{cases} \end{equation*} This sequence is reminiscent of the famous Collatz sequence

    更新日期:2020-06-23
  • Robustness of Pisot-regular sequences
    arXiv.cs.FL Pub Date : 2020-06-19
    Émilie Charlier; Célia Cisternino; Manon Stipulanti

    We consider numeration systems based on a $d$-tuple $\mathbf{U}=(U_1,\ldots,U_d)$ of sequences of integers and we define $(\mathbf{U},\mathbb{K})$-regular sequences through $\mathbb{K}$-recognizable formal series, where $\mathbb{K}$ is any semiring. We show that, for any $d$-tuple $\mathbf{U}$ of Pisot numeration systems and any commutative semiring $\mathbb{K}$, this definition does not depend on

    更新日期:2020-06-22
  • Effective Formal Verification of Neural Networks using the Geometry of Linear Regions
    arXiv.cs.FL Pub Date : 2020-06-18
    Haitham Khedr; James Ferlez; Yasser Shoukry

    Neural Networks (NNs) have increasingly apparent safety implications commensurate with their proliferation in real-world applications: both unanticipated as well as adversarial misclassifications can result in fatal outcomes. As a consequence, techniques of formal verification have been recognized as crucial to the design and deployment of safe NNs. In this paper, we introduce a new approach to formally

    更新日期:2020-06-22
  • Extremal overlap-free and extremal $β$-free binary words
    arXiv.cs.FL Pub Date : 2020-06-17
    Lucas Mol; Narad Rampersad; Jeffrey Shallit

    An overlap-free (or $\beta$-free) word $w$ over a fixed alphabet $\Sigma$ is extremal if every word obtained from $w$ by inserting a single letter from $\Sigma$ at any position contains an overlap (or a factor of exponent at least $\beta$, respectively). We find all lengths which admit an extremal overlap-free binary word. For every extended real number $\beta$ such that $2^+\leq\beta\leq 8/3$, we

    更新日期:2020-06-19
  • Symmetry Abstractions for Hybrid Systems and their Applications
    arXiv.cs.FL Pub Date : 2020-06-16
    Hussein Sibai; Sayan Mitra

    A symmetry of a dynamical system is a map that transforms one trajectory to another trajectory. We introduce a new type of abstraction for hybrid automata based on symmetries. The abstraction combines different modes in a concrete automaton A, whose trajectories are related by symmetries, into a single mode in the abstract automaton B. The abstraction sets the guard and reset of an abstract edge to

    更新日期:2020-06-18
  • Algebraic Language Theory for Eilenberg--Moore Algebras
    arXiv.cs.FL Pub Date : 2020-06-15
    Achim Blumensath

    We develop an algebraic language theory based on the notion of an Eilenberg--Moore algebra. In comparison to previous such frameworks the main contribution is the support for algebras with infinitely many sorts and the connection to logic in form of so-called `definable algebras'.

    更新日期:2020-06-15
  • Some complete $ω$-powers of a one-counter language, for any Borel class of finite rank
    arXiv.cs.FL Pub Date : 2020-06-15
    Olivier FinkelELM; Dominique LecomteIMJ

    We prove that, for any natural number n $\ge$ 1, we can find a finite alphabet $\Sigma$ and a finitary language L over $\Sigma$ accepted by a one-counter automaton, such that the $\omega$-power L $\infty$ := {w 0 w 1. .. $\in$ $\Sigma$ $\omega$ | $\forall$i $\in$ $\omega$ w i $\in$ L} is $\Pi$ 0 n-complete. We prove a similar result for the class $\Sigma$ 0 n .

    更新日期:2020-06-15
  • The undirected repetition threshold and undirected pattern avoidance
    arXiv.cs.FL Pub Date : 2020-06-12
    James D. Currie; Lucas Mol

    For a rational number $r$ such that $1

    更新日期:2020-06-12
  • The Look-and-Say The Biggest Sequence Eventually Cycles
    arXiv.cs.FL Pub Date : 2020-06-12
    Éric Brier; Rémi Géraud-Stewart; David Naccache; Alessandro Pacco; Emanuele Troiani

    In this paper we consider a variant of Conway's sequence (OEIS A005150, A006715) defined as follows: the next term in the sequence is obtained by considering contiguous runs of digits, and rewriting them as $ab$ where $b$ is the digit and $a$ is the maximum of $b$ and the run's length. We dub this the "look-and-say the biggest" (LSB) sequence. Conway's sequence is very similar ($b$ is just the run's

    更新日期:2020-06-12
  • Stuttering Conway Sequences Are Still Conway Sequences
    arXiv.cs.FL Pub Date : 2020-06-11
    Éric Brier; Rémi Géraud-Stewart; David Naccache; Alessandro Pacco; Emanuele Troiani

    A look-and-say sequence is obtained iteratively by reading off the digits of the current value, grouping identical digits together: starting with 1, the sequence reads: 1, 11, 21, 1211, 111221, 312211, etc. (OEIS A005150). Starting with any digit $d \neq 1$ gives Conway's sequence: $d$, $1d$, $111d$, $311d$, $13211d$, etc. (OEIS A006715). Conway popularised these sequences and studied some of their

    更新日期:2020-06-11
  • Avoiding abelian powers cyclically
    arXiv.cs.FL Pub Date : 2020-06-11
    Jarkko Peltomäki; Markus A. Whiteland

    We study a new notion of cyclic avoidance of abelian powers. A finite word $w$ avoids abelian $N$-powers cyclically if for each abelian $N$-power of period $m$ occurring in the infinite word $w^\omega$, we have $m \geq |w|$. Let $\mathcal{A}(k)$ be the least integer $N$ such that for all $n$ there exists a word of length $n$ over a $k$-letter alphabet that avoids abelian $N$-powers cyclically. Let

    更新日期:2020-06-11
  • On the complexity of the universality and inclusion problems for unambiguous context-free grammars (Invited Paper)
    arXiv.cs.FL Pub Date : 2020-06-09
    Lorenzo Clemente

    We study the computational complexity of universality and inclusion problems for unambiguous finite automata and context-free grammars. We observe that several such problems can be reduced to the universality problem for unambiguous context-free grammars. The latter problem has long been known to be decidable and we propose a PSPACE algorithm that works by reduction to the zeroness problem of recurrence

    更新日期:2020-06-09
  • Satisfiability and Model Checking for the Logic of Sub-Intervals under the Homogeneity Assumption
    arXiv.cs.FL Pub Date : 2020-06-08
    Laura Bozzelli; Alberto Molinari; Angelo Montanari; Adriano Peron; Pietro Sala

    The expressive power of interval temporal logics (ITLs) makes them really fascinating, and one of the most natural choices as specification and planning language. However, for a long time, due to their high computational complexity, they were considered not suitable for practical purposes. The recent discovery of several computationally well-behaved ITLs has finally changed the scenario. In this paper

    更新日期:2020-06-08
  • A Formal Definition of Stochastic Activity Networks Templates
    arXiv.cs.FL Pub Date : 2020-06-07
    Leonardo Montecchi; Paolo Lollini; Andrea Bondavalli

    Model-based evaluation has been extensively used to estimate performance and reliability metrics of computer systems, especially critical systems, for which experimental approaches are not always applicable. A significant challenge is constructing and maintaining the models for large-scale and possibly evolving systems. In a recent work we defined the Template Models Description Language (TMDL) framework

    更新日期:2020-06-07
  • Sumsets of Wythoff Sequences, Fibonacci Representation, and Beyond
    arXiv.cs.FL Pub Date : 2020-06-07
    Jeffrey Shallit

    Let $\alpha = (1+\sqrt{5})/2$ and define the lower and upper Wythoff sequences by $a_i = \lfloor i \alpha \rfloor$, $b_i = \lfloor i \alpha^2 \rfloor$ for $i \geq 1$. In a recent interesting paper, Kawsumarng et al. proved a number of results about numbers representable as sums of the form $a_i + a_j$, $b_i + b_j$, $a_i + b_j$, and so forth. In this paper I show how to derive all of their results,

    更新日期:2020-06-07
  • Temporal-Logic Query Checking over Finite Data Streams
    arXiv.cs.FL Pub Date : 2020-06-06
    Samuel Huang; Rance Cleaveland

    This paper describes a technique for inferring temporal-logic properties for sets of finite data streams. Such data streams arise in many domains, including server logs, program testing, and financial and marketing data; temporal-logic formulas that are satisfied by all data streams in a set can provide insight into the underlying dynamics of the system generating these streams. Our approach makes

    更新日期:2020-06-06
  • Provably Stable Interpretable Encodings of Context Free Grammars in RNNs with a Differentiable Stack
    arXiv.cs.FL Pub Date : 2020-06-05
    Dr. John Stogin; Ankur Mali; Dr. Lee Giles

    Given a collection of strings belonging to a context free grammar (CFG) and another collection of strings not belonging to the CFG, how might one infer the grammar? This is the problem of grammatical inference. Since CFGs are the languages recognized by pushdown automata (PDA), it suffices to determine the state transition rules and stack action rules of the corresponding PDA. An approach would be

    更新日期:2020-06-05
  • Twinning automata and regular expressions for string static analysis
    arXiv.cs.FL Pub Date : 2020-06-04
    Luca Negrini; Vincenzo Arceri; Pietro Ferrara; Agostino Cortesi

    In this paper we formalize and prove the soundness of Tarsis, a new abstract domain based on the abstract interpretation theory that approximates string values through finite state automata. The main novelty of Tarsis is that it works over an alphabet of strings instead of single characters. On the one hand, such approach requires a more complex and refined definition of the widening operator, and

    更新日期:2020-06-04
  • Solenoid Maps, Automatic Sequences, Van Der Put Series, and Mealy-Moore Automata
    arXiv.cs.FL Pub Date : 2020-06-03
    Rostislav Grigorchuk; Dmytro Savchuk

    The ring $\mathbb Z_d$ of $d$-adic integers has a natural interpretation as the boundary of a rooted $d$-ary tree $T_d$. Endomorphisms of this tree (i.e. solenoid maps) are in one-to-one correspondence with 1-Lipschitz mappings from $\mathbb Z_d$ to itself and automorphisms of $T_d$ constitute the group $\mathrm{Isom}(\mathbb Z_d)$. In the case when $d=p$ is prime, Anashin showed that $f\in\mathrm{Lip}^1(\mathbb

    更新日期:2020-06-03
  • On a Class of Constrained Synchronization Problems in NP
    arXiv.cs.FL Pub Date : 2020-06-02
    Stefan Hoffmann

    The class of known constraint automata for which the constrained synchronization problem is in NP all admit a special form. In this work, we take a closer look at them. We characterize a wider class of constraint automata that give constrained synchronization problems in NP, which encompasses all known problems in NP. We call these automata polycyclic automata. The corresponding language class of polycyclic

    更新日期:2020-06-02
  • Aperiodicity, Star-freeness, and First-order Definability of Structured Context-Free Languages
    arXiv.cs.FL Pub Date : 2020-06-01
    Dino MandrioliPolitecnico di Milano; Matteo PradellaPolitecnico di MilanoCNR-IEIIT; Stefano Crespi ReghizziPolitecnico di MilanoCNR-IEIIT

    A classic result in formal language theory is the equivalence among noncounting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic. Together with first-order completeness of linear temporal logic these results constitute a theoretical foundation for model-checking algorithms. Extending these results to structured subclasses of context-free

    更新日期:2020-06-01
  • Preservation of normality by unambiguous transducers
    arXiv.cs.FL Pub Date : 2020-05-29
    Olivier Carton

    We consider finite state non-determinisitic but unabiguous transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality of sequences of symbols. When these transducers are strongly connected, and when the input is a Borel normal sequence, the output is a sequence in which every block has a frequency given by a weighted automaton over the rationals. We provide

    更新日期:2020-05-29
  • From Functional Nondeterministic Transducers to Deterministic Two-Tape Automata
    arXiv.cs.FL Pub Date : 2020-05-27
    Elisabet Burjons; Fabian Frei; Martin Raszyk

    The question whether P = NP revolves around the discrepancy between active production and mere verification by Turing machines. In this paper, we examine the analogous problem for finite transducers and automata. Every nondeterministic finite transducer defines a binary relation associating input words with output words that are computed and accepted by the transducer. Functional transducers are those

    更新日期:2020-05-27
  • Timed Automata Benchmark Description
    arXiv.cs.FL Pub Date : 2020-05-27
    Peter Fontana; Rance Cleaveland

    This report contains the descriptions of the timed automata (models) and the properties (specifications) that are used as the "benchmark examples in Data structure choices for on-the-fly model checking of real-time systems" and "The power of proofs: New algorithms for timed automata model checking." The four models from those sources are: CSMA, FISCHER, LEADER, and GRC. Additionally we include in this

    更新日期:2020-05-27
  • Global Guidance for Local Generalization in Model Checking
    arXiv.cs.FL Pub Date : 2020-05-27
    Hari Govind V K; YuTing Chen; Sharon Shoham; Arie Gurfinkel

    SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition relation of a system, while employing SMT-based procedures, such as interpolation, to mitigate the limitations of local reasoning and allow for better generalization

    更新日期:2020-05-27
  • Structural Reductions Revisited
    arXiv.cs.FL Pub Date : 2020-05-26
    Yann Thierry-MiegSU, CNRS

    Structural reductions are a powerful class of techniques that reason on a specification with the goal to reduce it before attempting to explore its behaviors. In this paper we present new structural reduction rules for verification of deadlock freedom and safety properties of Petri nets. These new rules are presented together with a large body of rules found in diverse literature. For some rules we

    更新日期:2020-05-26
  • Verification and Validation of Convex Optimization Algorithms for Model Predictive Control
    arXiv.cs.FL Pub Date : 2020-05-26
    Raphaël CohenENAC; Eric FéronENAC; Pierre-Loïc GarocheENAC

    Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably stronger design constraints that arise when the applications of interest, such as aerospace systems, are safety-critical. Formal verification is the process of proving

    更新日期:2020-05-26
  • Verification of the IBOS Browser Security Properties in Reachability Logic
    arXiv.cs.FL Pub Date : 2020-05-25
    Stephen Skeirik; José Meseguer; Camilo Rocha

    This paper presents a rewriting logic specification of the Illinois Browser Operating System (IBOS) and defines several security properties, including the same-origin policy (SOP) in reachability logic. It shows how these properties can be deductively verified using our constructor-based reachability logic theorem prover. This paper also highlights the reasoning techniques used in the proof and three

    更新日期:2020-05-25
  • Symbolic coding of linear complexity for generic translations of the torus, using continued fractions
    arXiv.cs.FL Pub Date : 2020-05-25
    N. Pytheas Fogg; C. Noûs

    In this paper, we prove that almost every translation of $\mathbb{T}^2$ admits a symbolic coding which has linear complexity $2n+1$. The partitions are constructed with Rauzy fractals associated with sequences of substitutions, which are produced by a particular extended continued fraction algorithm in projective dimension $2$. More generally, in dimension $d\geq 1$, we study extended measured continued

    更新日期:2020-05-25
  • RTAMT: Online Robustness Monitors from STL
    arXiv.cs.FL Pub Date : 2020-05-24
    Dejan Nickovic; Tomoya Yamaguchi

    We present RTAMT, an online monitoring library for Signal Temporal Logic (STL) and its interface-aware variant (IA-STL), providing both discrete- and dense-time interpretation of the logic. We also introduce RTAMT4ROS, a tool that integrates RTAMT with Robotic Operating System (ROS), a common environment for developing robotic applications. We evaluate RTAMT and RTAMT4ROS on two robotic case studies

    更新日期:2020-05-24
  • An inequality for the number of periods in a word
    arXiv.cs.FL Pub Date : 2020-05-24
    Daniel Gabric; Narad Rampersad; Jeffrey Shallit

    We prove an inequality for the number of periods in a word x in terms of the length of x and its initial critical exponent. Next, we characterize all periods of the length-n prefix of a characteristic Sturmian word in terms of the lazy Ostrowski representation of n, and use this result to show that our inequality is tight for infinitely many words x. We propose two related measures of periodicity for

    更新日期:2020-05-24
  • Minimisation in Logical Form
    arXiv.cs.FL Pub Date : 2020-05-23
    Nick Bezhanishvili; Marcello Bonsangue; Helle Hvid Hansen; Dexter Kozen; Clemens Kupke; Prakash Panangaden; Alexandra Silva

    Stone-type dualities provide a powerful mathematical framework for studying properties of logical systems. They have recently been fruitfully explored in understanding minimisation of various types of automata. In Bezhanishvili et al. (2012), a dual equivalence between a category of coalgebras and a category of algebras was used to explain minimisation. The algebraic semantics is dual to a coalgebraic

    更新日期:2020-05-23
  • Primitive Sets of Words
    arXiv.cs.FL Pub Date : 2020-05-20
    Giuseppa Castiglione; Gabriele Fici; Antonio Restivo

    Given a (finite or infinite) subset $X$ of the free monoid $A^*$ over a finite alphabet $A$, the rank of $X$ is the minimal cardinality of a set $F$ such that $X \subseteq F^*$. We say that a submonoid $M$ generated by $k$ elements of $A^*$ is {\em $k$-maximal} if there does not exist another submonoid generated by at most $k$ words containing $M$. We call a set $X \subseteq A^*$ {\em primitive} if

    更新日期:2020-05-20
  • Infinitude of Primes Using Formal Language Theory
    arXiv.cs.FL Pub Date : 2020-05-20
    Aalok Thakkar

    Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of these languages are then employed to prove that there are infinitely many prime numbers.

    更新日期:2020-05-20
  • DisCoveR: Accurate & Efficient Discovery of Declarative Process Models
    arXiv.cs.FL Pub Date : 2020-05-20
    Christoffer Olling Back; Tijs Slaats; Thomas Troels Hildebrandt; Morten Marquard

    Declarative process modeling formalisms - which capture high-level process constraints - have seen growing interest, especially for modeling flexible processes. This paper presents DisCoveR, an extremely efficient and accurate declarative miner for learning Dynamic Condition Response (DCR) Graphs from event logs. We precisely formalize the algorithm, describe a highly efficient bit vector implementation

    更新日期:2020-05-20
  • Decidability and k-Regular Sequences
    arXiv.cs.FL Pub Date : 2020-05-19
    Daniel Krenn; Jeffrey Shallit

    In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from - lower and upper bounds on growth rate; in particular boundedness, - images, - regularity (recognizability by a deterministic finite automaton) of preimages, and - factors, such as squares and palindromes of such sequences. We show that the decision problems are undecidable

    更新日期:2020-05-19
  • On Weighted Prefix Normal Words
    arXiv.cs.FL Pub Date : 2020-05-19
    Yannik Eikmeier; Pamela Fleischmann; Dirk Nowotka

    A prefix normal word is a binary word whose prefixes contain at least as many 1s as any of its factors of the same length. Introduced by Fici and Lipt\'ak in 2011 the notion of prefix normality is so far only defined for words over the binary alphabet. In this work we investigate possible generalisations for finite words over arbitrary finite alphabets, namely weighted and subset prefix normality.

    更新日期:2020-05-19
  • A Frameless 2-Coloring of the Plane Lattice
    arXiv.cs.FL Pub Date : 2020-05-19
    Craig S. Kaplan; Jeffrey Shallit

    A picture frame in two dimensions is a rectangular array of symbols, with at least two rows and columns, where the first and last rows are identical, and the first and last columns are identical. If a coloring of the plane lattice has no picture frames, we call it frameless. In this note we show how to create a simple 2-coloring of the plane lattice that is frameless.

    更新日期:2020-05-19
  • On the Separability Problem of String Constraints
    arXiv.cs.FL Pub Date : 2020-05-18
    Parosh Aziz Abdulla; Mohamed Faouzi Atig; Vruda Dave; Shankara Narayanan Krishna

    We address the separability problem for straight-line string constraints. The separability problem for languages of a class C by a class S asks: given two languages A and B in C, does there exist a language I in S separating A and B (i.e., I is a superset of A and disjoint from B)? The separability of string constraints is the same as the fundamental problem of interpolation for string constraints

    更新日期:2020-05-18
  • On the Power of Unambiguity in Büchi Complementation
    arXiv.cs.FL Pub Date : 2020-05-18
    Yong Li; Moshe Y. Vardi; Lijun Zhang

    In this work, we exploit the power of unambiguity for the complementation problem of B\"uchi automata by utilizing reduced run directed acyclic graphs (DAGs) over infinite words, in which each vertex has at most one predecessor. Given a B\"uchi automaton with n states and a finite degree of ambiguity, we show that the number of states in the complementary B\"uchi automaton constructed by the classical

    更新日期:2020-05-18
  • Separation of Memory and Processing in Dual Recurrent Neural Networks
    arXiv.cs.FL Pub Date : 2020-05-17
    Christian Oliva; Luis F. Lago-Fernández

    We explore a neural network architecture that stacks a recurrent layer and a feedforward layer that is also connected to the input, and compare it to standard Elman and LSTM architectures in terms of accuracy and interpretability. When noise is introduced into the activation function of the recurrent units, these neurons are forced into a binary activation regime that makes the networks behave much

    更新日期:2020-05-17
  • On the Origin of Quantum Uncertainty
    arXiv.cs.FL Pub Date : 2020-05-15
    Christoph AdamiMichigan State University

    I propose that quantum uncertainty is a manifestation of the indeterminism inherent in mathematical logic.

    更新日期:2020-05-15
  • Qualitative Controller Synthesis for Consumption Markov Decision Processes
    arXiv.cs.FL Pub Date : 2020-05-14
    František Blahoudek; Tomáš Brázdil; Petr Novotný; Melkior Ornik; Pranay Thangeda; Ufuk Topcu

    Consumption Markov Decision Processes (CMDPs) are probabilistic decision-making models of resource-constrained systems. In a CMDP, the controller possesses a certain amount of a critical resource, such as electric power. Each action of the controller can consume some amount of the resource. Resource replenishment is only possible in special reload states, in which the resource level can be reloaded

    更新日期:2020-05-14
  • Structural Equivalences for Reversible Calculi of Communicating Systems (Oral communication)
    arXiv.cs.FL Pub Date : 2020-05-14
    Clément Aubert; Ioana Cristescu

    The formalization of process algebras usually starts with a minimal core of operators and rules for its transition system, and then relax the system to improve its usability and ease the proofs. In the calculus of communicating systems (CCS), the structural congruence plays this role by making e.g. parallel composition commutative and associative: without it, the system would be cumbersome to use and

    更新日期:2020-05-14
  • How Reversibility Can Solve Traditional Questions: The Example of Hereditary History-Preserving Bisimulation
    arXiv.cs.FL Pub Date : 2020-05-14
    Clément AubertHMS; Ioana CristescuHMS

    Reversible computation opens up the possibility of overcoming some of the hardware's current physical limitations. It also offers theoretical insights, as it enriches multiple paradigms and models of computation, and sometimes retrospectively enlightens them. Concurrent reversible computation, for instance, offered interesting extensions to the Calculus of Communicating Systems, but was still lacking

    更新日期:2020-05-14
  • Bisimilarity in fresh-register automata
    arXiv.cs.FL Pub Date : 2020-05-13
    Andrzej S. Murawski; Steven J. Ramsay; Nikos Tzevelekos

    Register automata are a basic model of computation over infinite alphabets. Fresh-register automata extend register automata with the capability to generate fresh symbols in order to model computational scenarios involving name creation. This paper investigates the complexity of the bisimilarity problem for classes of register and fresh-register automata. We examine all main disciplines that have appeared

    更新日期:2020-05-13
  • Bisimulation Finiteness of Pushdown Systems Is Elementary
    arXiv.cs.FL Pub Date : 2020-05-13
    Stefan Göller; Paweł Parys

    We show that in case a pushdown system is bisimulation equivalent to a finite system, there is already a bisimulation equivalent finite system whose size is elementarily bounded in the description size of the pushdown system. As a consequence we obtain that it is elementarily decidable if a given pushdown system is bisimulation equivalent to some finite system. This improves a previously best-known

    更新日期:2020-05-13
  • Probabilistic Hyperproperties with Nondeterminism
    arXiv.cs.FL Pub Date : 2020-05-13
    Erika Abraham; Ezio Bartocci; Borzoo Bonakdarpour; Oyendrila Dobe

    We study the problem of formalizing and checking probabilistic hyperproperties for models that allow nondeterminism in actions. We extend the temporal logic HyperPCTL, which has been previously introduced for discrete-time Markov chains, to enable the specification of hyperproperties also for Markov decision processes. We generalize HyperPCTL by allowing explicit and simultaneous quantification over

    更新日期:2020-05-13
  • Constraint Synchronization with Two or Three State Partial Constraint Automata
    arXiv.cs.FL Pub Date : 2020-05-12
    Stefan Hoffmann

    Here, we study the question if synchronizing words exist that belong to some fixed constraint language, given by some partial finite automaton called constraint automaton. We strengthen a previous result by giving a complete classification of the computational complexity landscape for constraint automata with two states and an arbitrary alphabet. We also give a classification for three state automata

    更新日期:2020-05-12
  • N-PAT: A Nested Model-Checker
    arXiv.cs.FL Pub Date : 2020-05-12
    Hadrien Bride; Cheng-Hao Cai; Jin Song Dong; Rajeev Gore; Zhé Hóu; Brendan Mahony; Jim McCarthy

    N-PAT is a new model-checking tool that supports the verification of nested-models, i.e. models whose behaviour depends on the results of verification tasks. In this paper, we describe its operation and discuss mechanisms that are tailored to the efficient verification of nested-models. Further, we motivate the advantages of N-PAT over traditional model-checking tools through a network security case

    更新日期:2020-05-12
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