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  • On-Line Permissive Supervisory Control of Discrete Event Systems for scLTL Specifications
    arXiv.cs.FL Pub Date : 2020-03-26
    Ami Sakakibara; Toshimitsu Ushio

    We propose an on-line supervisory control scheme for discrete event systems (DESs), where a control specification is described by a fragment of linear temporal logic. On the product automaton of the DES and an acceptor for the specification, we define a ranking function that returns the minimum number of steps required to reach an accepting state from each state. In addition, we introduce a permissiveness

    更新日期:2020-03-28
  • Minimising Good-for-Games automata is NP complete
    arXiv.cs.FL Pub Date : 2020-03-26
    Sven Schewe

    This paper discusses the hardness of finding minimal good-for-games (GFG) Buchi, Co-Buchi, and parity automata with state based acceptance. The problem appears to sit between finding small deterministic and finding small nondeterministic automata, where minimality is NP-complete and PSPACE-complete, respectively. However, recent work of Radi and Kupferman has shown that minimising Co-Buchi automata

    更新日期:2020-03-28
  • Equivalence checking for weak bi-Kleene algebra
    arXiv.cs.FL Pub Date : 2018-07-05
    Tobias Kappé; Paul Brunet; Bas Luttik; Alexandra Silva; Fabio Zanasi

    Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational

    更新日期:2020-03-28
  • Learning One-Clock Timed Automata
    arXiv.cs.FL Pub Date : 2019-10-23
    Jie An; Mingshuai Chen; Bohua Zhan; Naijun Zhan; Miaomiao Zhang

    We present an algorithm for active learning of deterministic timed automata with a single clock. The algorithm is within the framework of Angluin's $L^*$ algorithm and inspired by existing work on the active learning of symbolic automata. Due to the need of guessing for each transition whether it resets the clock, the algorithm is of exponential complexity in the size of the learned automata. Before

    更新日期:2020-03-27
  • Efficient Automata-based Planning and Control under Spatio-Temporal Logic Specifications
    arXiv.cs.FL Pub Date : 2019-09-24
    Lars Lindemann; Dimos V. Dimarogonas

    The use of spatio-temporal logics in control is motivated by the need to impose complex spatial and temporal behavior on dynamical systems, and to control these systems accordingly. Synthesizing correct-by-design control laws is a challenging task resulting in computationally demanding methods. We consider efficient automata-based planning for continuous-time systems under signal interval temporal

    更新日期:2020-03-26
  • Kontrol Edilebilir ptSTL Formulu Sentezi -- Synthesis of Controllable ptSTL Formulas
    arXiv.cs.FL Pub Date : 2020-03-22
    Irmak Saglam; Ebru Aydin Gol

    In this work, we develop an approach to anomaly detection and prevention problem using Signal Temporal Logic (STL). This approach consists of two steps: detection of the causes of the anomalities as STL formulas and prevention of the satisfaction of the formula via controller synthesis. This work focuses on the first step and proposes a formula template such that any controllable cause can be represented

    更新日期:2020-03-24
  • A Physically Universal Turing Machine
    arXiv.cs.FL Pub Date : 2020-03-20
    Ville Salo; Ilkka Törmä

    We construct a two-dimensional Turing machine that is physically universal in both the moving tape and moving head model. In particular, it is mixing of all finite orders in both models. We also provide a variant that is physically universal in the moving tape model, but not in the moving head model.

    更新日期:2020-03-24
  • The Strahler number of a parity game
    arXiv.cs.FL Pub Date : 2020-03-19
    Laure Daviaud; Marcin Jurdziński; K. S. Thejaswini

    The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. It is proved that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices~$n$ and linear in $({d}/{2k})^k$

    更新日期:2020-03-20
  • The State Complexity of Lexicographically Smallest Words and Computing Successors
    arXiv.cs.FL Pub Date : 2020-03-18
    Lukas Fleischer; Jeffrey Shallit

    Given a regular language L over an ordered alphabet $\Sigma$, the set of lexicographically smallest (resp., largest) words of each length is itself regular. Moreover, there exists an unambiguous finite-state transducer that, on a given word w, outputs the length-lexicographically smallest word larger than w (henceforth called the L-successor of w). In both cases, naive constructions result in an exponential

    更新日期:2020-03-19
  • Towards a Uniform Theory of Effectful State Machines
    arXiv.cs.FL Pub Date : 2014-01-21
    Sergey Goncharov; Stefan Milius; Alexandra Silva

    Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs' notion of a T-automaton, where T is a monad. We show that the generic language semantics for T-automata correctly instantiates the usual

    更新日期:2020-03-18
  • Cerny-Starke conjecture from the sixties of XX century
    arXiv.cs.FL Pub Date : 2020-03-13
    A. N. Trahtman

    A word $w$ of letters on edges of underlying graph $\Gamma$ of deterministic finite automaton (DFA) is called synchronizing if $w$ sends all states of the automaton to a unique state. J. \v{C}erny discovered in 1964 a sequence of $n$-state complete DFA possessing a minimal synchronizing word of length $(n-1)^2$. The hypothesis, well known today as \v{C}erny conjecture, claims that $(n-1)^2$ is a precise

    更新日期:2020-03-16
  • Stable variation in multidimensional competition
    arXiv.cs.FL Pub Date : 2020-03-11
    Henri Kauhanen

    The Fundamental Theorem of Language Change (Yang, 2000) implies the impossibility of stable variation in the Variational Learning framework, but only in the special case where two, and not more, grammatical variants compete. Introducing the notion of an advantage matrix, I generalize Variational Learning to situations where the learner receives input generated by more than two grammars, and show that

    更新日期:2020-03-16
  • On the Balancedness of Tree-to-word Transducers
    arXiv.cs.FL Pub Date : 2019-11-29
    Raphaela Löbel; Michael Luttenberger; Helmut Seidl

    A language over an alphabet $B = A \cup \overline{A}$ of opening ($A$) and closing ($\overline{A}$) brackets, is balanced if it is a subset of the Dyck language $D_B$ over $B$, and it is well-formed if all words are prefixes of words in $D_B$. We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial

    更新日期:2020-03-16
  • Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata
    arXiv.cs.FL Pub Date : 2019-09-12
    Augusto Modanese

    After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors whose acceptance condition depends on the states of all cells in the automaton. We prove a time hierarchy theorem for sublinear-time ACA classes, analyze their intersection

    更新日期:2020-03-16
  • Four heads are better than three
    arXiv.cs.FL Pub Date : 2020-03-12
    Ville Salo

    We construct recursively-presented finitely-generated torsion groups which have bounded torsion and whose word problem is conjunctive equivalent (in particular positive and Turing equivalent) to a given recursively enumerable set. These groups can be interpreted as groups of finite state machines or as subgroups of topological full groups, on effective subshifts over other torsion groups. We define

    更新日期:2020-03-16
  • Dependently Typed Knowledge Graphs
    arXiv.cs.FL Pub Date : 2020-03-08
    Zhangsheng Lai; Aik Beng Ng; Liang Ze Wong; Simon See; Shaowei Lin

    Reasoning over knowledge graphs is traditionally built upon a hierarchy of languages in the Semantic Web Stack. Starting from the Resource Description Framework (RDF) for knowledge graphs, more advanced constructs have been introduced through various syntax extensions to add reasoning capabilities to knowledge graphs. In this paper, we show how standardized semantic web technologies (RDF and its query

    更新日期:2020-03-10
  • Residual Nominal Automata
    arXiv.cs.FL Pub Date : 2019-10-25
    Joshua Moerman; Matteo Sammartino

    Nominal automata are models for accepting languages over infinite alphabets. In this paper we refine the hierarchy of nondeterministic nominal automata, by developing the theory of residual nominal automata. In particular, we show that they admit canonical minimal representatives, and that the universality problem becomes decidable. We also study exact learning of these automata, and settle questions

    更新日期:2020-03-06
  • Undecidability of model-checking branching-time properties of stateless probabilistic pushdown process
    arXiv.cs.FL Pub Date : 2014-05-19
    Tianrong Lin

    In this paper, we settle a problem in probabilistic verification of infinite--state process (specifically, {\it probabilistic pushdown process}). We show that model checking {\it stateless probabilistic pushdown process} (pBPA) against {\it probabilistic computational tree logic} (PCTL) is undecidable.

    更新日期:2020-03-04
  • A spatio-temporalisation of ALC(D) and its translation into alternating automata augmented with spatial constraints
    arXiv.cs.FL Pub Date : 2020-02-22
    Amar Isli

    The aim of this work is to provide a family of qualitative theories for spatial change in general, and for motion of spatial scenes in particular. To achieve this, we consider a spatio-temporalisation MTALC(Dx), of the well-known ALC(D) family of Description Logics (DLs) with a concrete domain: the MTALC(Dx) concepts are interpreted over infinite k-ary Sigma-trees, with the nodes standing for time

    更新日期:2020-03-02
  • Hyperproperties for Robotics: Planning via HyperLTL
    arXiv.cs.FL Pub Date : 2019-11-26
    Yu Wang; Siddhartha Nalluri; Miroslav Pajic

    There is a growing interest on formal methods-based robotic planning for temporal logic objectives. In this work, we extend the scope of existing synthesis methods to hyper-temporal logics. We are motivated by the fact that important planning objectives, such as optimality, robustness, and privacy, (maybe implicitly) involve the interrelation between multiple paths. Such objectives are thus hyperproperties

    更新日期:2020-03-02
  • Extracting Automata from Recurrent Neural Networks Using Queries and Counterexamples
    arXiv.cs.FL Pub Date : 2017-11-27
    Gail Weiss; Yoav Goldberg; Eran Yahav

    We present a novel algorithm that uses exact learning and abstraction to extract a deterministic finite automaton describing the state dynamics of a given trained RNN. We do this using Angluin's L* algorithm as a learner and the trained RNN as an oracle. Our technique efficiently extracts accurate automata from trained RNNs, even when the state vectors are large and require fine differentiation.

    更新日期:2020-02-28
  • Buchi automata augmented with spatial constraints: simulating an alternating with a nondeterministic and deciding the emptiness problem for the latter
    arXiv.cs.FL Pub Date : 2020-02-22
    Amar Isli

    The aim of this work is to thoroughly investigate Buchi automata augmented with spatial constraints. The input trees of such an automaton are infinite k-ary Sigma-trees, with the nodes standing for time points, and Sigma including, additionally to its uses in classical k-ary Sigma-trees, the description of the snapshot of an n-object spatial scene of interest. The constraints, from an RCC8-like spatial

    更新日期:2020-02-27
  • Near Optimal Task Graph Scheduling with Priced Timed Automata and Priced Timed Markov Decision Processes
    arXiv.cs.FL Pub Date : 2020-02-25
    Anne Ejsing; Martin Jensen; Marco Muñiz; Jacob Nørhave; Lars Rechter

    Task graph scheduling is a relevant problem in computer science with application to diverse real world domains. Task graph scheduling suffers from a combinatorial explosion and thus finding optimal schedulers is a difficult task. In this paper we present a methodology for computing near-optimal preemptive and non-preemptive schedulers for task graphs. The task graph scheduling problem is reduced to

    更新日期:2020-02-26
  • Gowers norms for automatic sequences
    arXiv.cs.FL Pub Date : 2020-02-21
    Jakub Byszewski; Jakub Konieczny; Clemens Müllner

    We show that any automatic sequence can be separated into a structured part and a Gowers uniform part in a way that is considerably more efficient than guaranteed by the Arithmetic Regularity Lemma. For sequences produced by strongly connected and prolongable automata, the structured part is rationally almost periodic, while for general sequences the description is marginally more complicated. In particular

    更新日期:2020-02-25
  • Automata for Hyperlanguages
    arXiv.cs.FL Pub Date : 2020-02-23
    Borzoo Bonakdarpour; Sarai Sheinvald

    Hyperproperties lift conventional trace properties from a set of execution traces to a set of sets of execution traces. Hyperproperties have been shown to be a powerful formalism for expressing and reasoning about information-flow security policies and important properties of cyber-physical systems such as sensitivity and robustness, as well as consistency conditions in distributed computing such as

    更新日期:2020-02-25
  • How Good Is a Strategy in a Game With Nature?
    arXiv.cs.FL Pub Date : 2020-02-23
    Arnaud Carayol; Olivier Serre

    We consider games with two antagonistic players --- \'Elo\"ise (modelling a program) and Ab\'elard (modelling a byzantine environment) --- and a third, unpredictable and uncontrollable player, that we call Nature. Motivated by the fact that the usual probabilistic semantics very quickly leads to undecidability when considering either infinite game graphs or imperfect-information, we propose two alternative

    更新日期:2020-02-25
  • First-order tree-to-tree functions
    arXiv.cs.FL Pub Date : 2020-02-21
    Mikołaj Bojańczyk; Amina Doumane

    We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as tree-to-tree homomorphisms or pre-order traversal, by using combinators such as function composition.

    更新日期:2020-02-24
  • Extensions of $ω$-Regular Languages
    arXiv.cs.FL Pub Date : 2020-02-21
    Mikołaj Bojańczyk; Edon Kelmendi; Rafał Stefański; Georg Zetzsche

    We consider extensions of monadic second order logic over $\omega$-words, which are obtained by adding one language that is not $\omega$-regular. We show that if the added language $L$ has a neutral letter, then the resulting logic is necessarily undecidable. A corollary is that the $\omega$-regular languages are the only decidable Boolean-closed full trio over $\omega$-words.

    更新日期:2020-02-24
  • On polynomial recursive sequences
    arXiv.cs.FL Pub Date : 2020-02-20
    Michaël Cadilhac; Filip Mazowiecki; Charles Paperman; Michał Pilipczuk; Géraud Sénizergues

    We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is b_n=n!. Our main result is that the sequence u_n=n^n

    更新日期:2020-02-21
  • Multiplicity Equivalence Testing of Automata over Partially Commutative Monoids
    arXiv.cs.FL Pub Date : 2020-02-20
    V. Arvind; Abhranil Chatterjee; Rajit Datta; Partha Mukhopadhyay

    We study \emph{multiplicity equivalence} testing of automata over partially commutative monoids (pc monoids) and show efficient algorithms in special cases, exploiting the structure of the underlying non-commutation graph of the monoid. Specifically, if the clique cover number of the non-commutation graph (the minimum number of cliques covering the graph) of the pc monoid is a constant, we obtain a

    更新日期:2020-02-21
  • From Stateless to Stateful Priorities: Technical Report
    arXiv.cs.FL Pub Date : 2020-02-20
    Christian Herrera

    We present the notion of stateful priorities for imposing precise restrictions on system actions, in order to meet safety constraints. By using stateful priorities we are able to exclusively restrict erroneous system behavior as specified by the constraint, whereas safe system behavior remains unrestricted. Given a system modeled as a network of discrete automata and an error constraint, we present

    更新日期:2020-02-21
  • Combining Partial Specifications using Alternating Interface Automata
    arXiv.cs.FL Pub Date : 2020-02-20
    Ramon Janssen

    To model real-world software systems, modelling paradigms should support a form of compositionality. In interface theory and model-based testing with inputs and outputs, conjunctive operators have been introduced: the behaviour allowed by composed specification s1 $\wedge$ s2 is the behaviour allowed by both partial models s1 and s2. The models at hand are non-deterministic interface automata, but

    更新日期:2020-02-21
  • The Complexity of Aggregates over Extractions by Regular Expressions
    arXiv.cs.FL Pub Date : 2020-02-20
    Johannes Doleschal; Noa Bratman; Benny Kimelfeld; Wim Martens

    Regular expressions with capture variables, also known as "regex formulas," extract relations of spans (intervals identified by their start and end indices) from text. Based on these Fagin et al. introduced regular document spanners which are the closure of regex formulas under Relational Algebra. In this work, we study the computational complexity of querying text by aggregate functions, like sum

    更新日期:2020-02-21
  • Continuity of Functional Transducers: A Profinite Study of Rational Functions
    arXiv.cs.FL Pub Date : 2018-02-28
    Michaël Cadilhac; Olivier Carton; Charles Paperman

    A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the characterization of the sequential transducers computable in some circuit complexity classes. Here, we report on the decidability of continuity for functional transducers

    更新日期:2020-02-21
  • On Computability of Data Word Functions Defined by Transducers
    arXiv.cs.FL Pub Date : 2020-02-19
    Léo Exibard; Emmanuel Filiot; Pierre-Alain Reynier

    In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data omega-words). The notion of computability is defined through Turing machines with infinite inputs which can produce the corresponding infinite outputs in the limit. We use non-deterministic transducers equipped with registers, an extension of register automata with outputs

    更新日期:2020-02-20
  • Comparing consecutive letter counts in multiple context-free languages
    arXiv.cs.FL Pub Date : 2020-02-19
    Florian Lehner; Christian Lindorfer

    Context-free grammars are not able to model cross-serial dependencies in natural languages. To overcome this issue, Seki et al. introduced a generalization called $m$-multiple context-free grammars ($m$-MCFGs), which deal with $m$-tuples of strings. We show that $m$-MCFGs are capable of comparing the number of consecutive occurrences of at most $2m$ different letters. In particular, the language $\{a_1^{n_1}

    更新日期:2020-02-20
  • Automaticity and invariant measures of linear cellular automata
    arXiv.cs.FL Pub Date : 2018-11-03
    Eric Rowland; Reem Yassawi

    We show that spacetime diagrams of linear cellular automata $\Phi : {\mathbb F}_p^{\mathbb Z} \to {\mathbb F}_p^{\mathbb Z}$ with $(-p)$-automatic initial conditions are automatic. This extends existing results on initial conditions which are eventually constant. Each automatic spacetime diagram defines a $(\sigma, \Phi)$-invariant subset of ${\mathbb F}_p^{\mathbb Z}$, where $\sigma$ is the left shift

    更新日期:2020-02-20
  • The upper density of an automatic set is rational
    arXiv.cs.FL Pub Date : 2020-02-17
    Jason P. Bell

    Given a natural number $k\ge 2$ and a $k$-automatic set $S$ of natural numbers, we show that the lower density and upper density of $S$ are recursively computable rational numbers and we provide an algorithm for computing these quantities. In addition, we show that for every natural number $k\ge 2$ and every pair of rational numbers $(\alpha,\beta)$ with $0<\alpha<\beta<1$ or with $(\alpha,\beta)\in

    更新日期:2020-02-19
  • Playing Against Opponents With Limited Memory
    arXiv.cs.FL Pub Date : 2020-02-17
    Dhananjay Raju; Rüdiger Ehlers; Ufuk Topcu

    We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the environment player is not genuinely adversarial to the system player. The environment player has goals of its own, but the exact goal of the environment player is

    更新日期:2020-02-19
  • On Succinctness and Recognisability of Alternating Good-for-Games Automata
    arXiv.cs.FL Pub Date : 2020-02-17
    Udi Boker; Denis Kuperberg; Karoliina Lehtinen; Michał Skrzypczak

    We study alternating good-for-games (GFG) automata, i.e., alternating automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the suffix of the input word still to be read. We show that they can be exponentially more succinct than both their nondeterministic and universal counterparts. Furthermore, we lift many results from nondeterministic

    更新日期:2020-02-19
  • Synthesis in Presence of Dynamic Links
    arXiv.cs.FL Pub Date : 2020-02-18
    Béatrice Bérard; Benedikt Bollig; Patricia Bouyer; Matthias Függer; Nathalie Sznajder

    The problem of distributed synthesis is to automatically generate a distributed algorithm, given a target communication network and a specification of the algorithm's correct behavior. Previous work has focused on static networks with an apriori fixed message size. This approach has two shortcomings: Recent work in distributed computing is shifting towards dynamically changing communication networks

    更新日期:2020-02-19
  • Regular resynchronizability of origin transducers is undecidable
    arXiv.cs.FL Pub Date : 2020-02-18
    Denis Kuperberg; Jan Martens

    We study the relation of containment up to unknown regular resynchronization between two-way non-deterministic transducers. We show that it constitutes a preorder, and that the corresponding equivalence relation is properly intermediate between origin equivalence and classical equivalence. We give a syntactical characterization for containment of two transducers up to resynchronization, and use it

    更新日期:2020-02-19
  • Better Automata through Process Algebra
    arXiv.cs.FL Pub Date : 2020-02-18
    Rance Cleaveland

    This paper shows how the use of Structural Operational Semantics (SOS) in the style popularized by the process-algebra community can lead to a more succinct and useful construction for building finite automata from regular expressions. Such constructions have been known for decades, and form the basis for the proofs of one direction of Kleene's Theorem. The purpose of the new construction is, on the

    更新日期:2020-02-19
  • The Post Correspondence Problem and equalisers for certain free group and monoid morphisms
    arXiv.cs.FL Pub Date : 2020-02-18
    Laura Ciobanu; Alan D. Logan

    A marked free monoid morphism is a morphism for which the image of each generator starts with a different letter, and immersions are the analogous maps in free groups. We show that the (simultaneous) PCP is decidable for immersions of free groups, and provide an algorithm to compute bases for the sets, called equalisers, on which the immersions take the same values. We also answer a question of Stallings

    更新日期:2020-02-19
  • Distributed graph problems through an automata-theoretic lens
    arXiv.cs.FL Pub Date : 2020-02-18
    Yi-Jun Chang; Jan Studený; Jukka Suomela

    We study the following algorithm synthesis question: given the description of a locally checkable graph problem $\Pi$ for paths or cycles, determine in which instances $\Pi$ is solvable, determine what is the distributed round complexity of solving $\Pi$ in the usual $\mathsf{LOCAL}$ model of distributed computing, and construct an asymptotically optimal distributed algorithm for solving $\Pi$. To

    更新日期:2020-02-19
  • Decidability of cutpoint isolation for letter-monotonic probabilistic finite automata
    arXiv.cs.FL Pub Date : 2020-02-18
    Paul C. Bell; Pavel Semukhin

    We show the surprising result that the cutpoint isolation problem is decidable for probabilistic finite automata where input words are taken from a letter-monotonic context-free language. A context-free language $L$ is letter-monotonic when $L \subseteq a_1^*a_2^* \cdots a_\ell^*$ for some finite $\ell > 0$ where each letter is distinct. A cutpoint is isolated when it cannot be approached arbitrarily

    更新日期:2020-02-19
  • Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications
    arXiv.cs.FL Pub Date : 2019-11-19
    Suguman Bansal; Yong Li; Lucas M. Tabajara; Moshe Y. Vardi

    LTLf synthesis is the automated construction of a reactive system from a high-level description, expressed in LTLf, of its finite-horizon behavior. So far, the conversion of LTLf formulas to deterministic finite-state automata (DFAs) has been identified as the primary bottleneck to the scalabity of synthesis. Recent investigations have also shown that the size of the DFA state space plays a critical

    更新日期:2020-02-19
  • Transfinite Lyndon words
    arXiv.cs.FL Pub Date : 2018-09-24
    Olivier Carton; Luc Boasson

    In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a relaxation of the condition used in the case of finite words. In the annex, we prove that the factorization of a rational word has a special form and that it can be computed

    更新日期:2020-02-19
  • Information-Flow Interfaces
    arXiv.cs.FL Pub Date : 2020-02-15
    Ezio Bartocci; Thomas Ferrère; Thomas A. Henzinger; Dejan Nickovic; Ana Oliveira da Costa

    Contract-based design is a promising methodology for taming the complexity of developing sophisticated systems. A formal contract distinguishes between assumptions, which are constraints that the designer of a component puts on the environments in which the component can be used safely, and guarantees, which are promises that the designer asks from the team that implements the component. A theory of

    更新日期:2020-02-18
  • Four-valued monitorability of $ω$-regular languages
    arXiv.cs.FL Pub Date : 2020-02-17
    Zhe Chen; Yunyun Chen; Robert M. Hierons; Yifan Wu

    Runtime Verification (RV) is a lightweight formal technique in which program or system execution is monitored and analyzed, to check whether certain properties are satisfied or violated after a finite number of steps. The use of RV has led to interest in deciding whether a property is monitorable: whether it is always possible for the satisfaction or violation of the property to be determined after

    更新日期:2020-02-18
  • Equivalence of Dataflow Graphs via Rewrite Rules Using a Graph-to-Sequence Neural Model
    arXiv.cs.FL Pub Date : 2020-02-17
    Steve Kommrusch; Théo Barollet; Louis-Noël Pouchet

    In this work we target the problem of provably computing the equivalence between two programs represented as dataflow graphs. To this end, we formalize the problem of equivalence between two programs as finding a set of semantics-preserving rewrite rules from one into the other, such that after the rewrite the two programs are structurally identical, and therefore trivially equivalent. We then develop

    更新日期:2020-02-18
  • Revisiting Underapproximate Reachability for Multipushdown Systems
    arXiv.cs.FL Pub Date : 2020-02-14
    S. Akshay; Paul Gastin; S Krishna; Sparsa Roychowdhury

    Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful behaviors. In this paper, we propose a new class of bounded under approximations for multi-pushdown systems, which subsumes most existing classes. We develop an efficient

    更新日期:2020-02-17
  • The computational power of parsing expression grammars
    arXiv.cs.FL Pub Date : 2019-02-21
    Bruno Loff; Nelma Moreira; Rogério Reis

    We study the computational power of parsing expression grammars (PEGs). We begin by constructing PEGs with unexpected behaviour, and surprising new examples of languages with PEGs, including the language of palindromes whose length is a power of two, and a binary-counting language. We then propose a new computational model, the scaffolding automaton, and prove that it exactly characterises the computational

    更新日期:2020-02-17
  • Theoretical Limitations of Self-Attention in Neural Sequence Models
    arXiv.cs.FL Pub Date : 2019-06-16
    Michael Hahn

    Transformers are emerging as the new workhorse of NLP, showing great success across tasks. Unlike LSTMs, transformers process input sequences entirely through self-attention. Previous work has suggested that the computational capabilities of self-attention to process hierarchical structures are limited. In this work, we mathematically investigate the computational power of self-attention to model formal

    更新日期:2020-02-14
  • Optimal Label Splitting for Embedding an LTS into an arbitrary Petri Net Reachability Graph is NP-complete
    arXiv.cs.FL Pub Date : 2020-02-12
    Uli Schlachter; Harro Wimmel

    For a given labelled transition system (LTS), synthesis is the task to find an unlabelled Petri net with an isomorphic reachability graph. Even when just demanding an embedding into a reachability graph instead of an isomorphism, a solution is not guaranteed. In such a case, label splitting is an option, i.e. relabelling edges of the LTS such that differently labelled edges remain different. With an

    更新日期:2020-02-13
  • NP Reasoning in the Monotone $μ$-Calculus
    arXiv.cs.FL Pub Date : 2020-02-12
    Daniel Hausmann; Lutz Schröder

    Satisfiability checking for monotone modal logic is known to be (only) NP-complete. We show that this remains true when the logic is extended with aconjunctive and alternation-free fixpoint operators as well as the universal modality; the resulting logic -- the aconjunctive alternation-free monotone $\mu$-calculus with the universal modality -- contains both concurrent propositional dynamic logic (CPDL)

    更新日期:2020-02-13
  • Minimization of visibly pushdown automata is NP-complete
    arXiv.cs.FL Pub Date : 2019-07-22
    Olivier Gauwin; Anca Muscholl; Michael Raskin

    We show that the minimization of visibly pushdown automata is NP-complete. This result is obtained by introducing immersions, that recognize multiple languages (over a usual, non-visible alphabet) using a common deterministic transition graph, such that each language is associated with an initial state and a set of final states. We show that minimizing immersions is NP-complete, and reduce this problem

    更新日期:2020-02-13
  • Collaboration vs. choreography conformance in BPMN
    arXiv.cs.FL Pub Date : 2020-02-06
    Flavio Corradini; Andrea Morichetta; Andrea Polini; Barbara Re; Francesco Tiezzi

    The BPMN 2.0 standard is a widely used semi-formal notation to model from different perspectives distributed information systems. Different diagrams are made available to represent such perspectives. Choreography diagrams represent global constraints concerning the interactions among system components without exposing their internal structure. Collaboration diagrams depict the internal behaviour of

    更新日期:2020-02-12
  • Polynomial time algorithms for inclusion and equivalence of deterministic parity acceptors
    arXiv.cs.FL Pub Date : 2020-02-08
    Dana Angluin; Dana Fisman

    The class of omega languages recognized by deterministic parity acceptors (DPAs) is exactly the regular omega languages. The inclusion problem is the following: given two DPAs P1 and P2, determine whether the language recognized by P1 is a subset of the language recognized by P2, and if not, return an ultimately periodic omega word accepted by P1 but not P2. We describe a polynomial time algorithm

    更新日期:2020-02-11
  • Alternating Tree Automata with Qualitative Semantics
    arXiv.cs.FL Pub Date : 2020-02-10
    Raphaël Berthon; Nathanaël Fijalkow; Emmanuel Filiot; Shibashis Guha; Bastien Maubert; Aniello Murano; Laureline Pinault; Sophie Pinchinat; Sasha Rubin; Olivier Serre

    We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this paper we prove a positive and a negative result for the emptiness problem of alternating

    更新日期:2020-02-11
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