Computer Science

So-called separation automata are in the core of several recently invented quasi-polynomial time algorithms for parity games. An explicit q -state separation automaton implies an algorithm for parity games with running time polynomial in q . It is open whether a polynomial-state separation automaton exists. A positive answer will lead to a polynomial-time algorithm for parity games, while a negative answer will at least demonstrate impossibility to construct such an algorithm using separation approach. In this work we prove exponential lower bound for a restricted class of separation automata. Our technique combines communication complexity and Kolmogorov complexity. One of our technical contributions belongs to extremal combinatorics. Namely, we prove a new upper bound on the product of sizes of two families of sets with small pairwise intersection.

By fundamental results of Schützenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata form a general and widely studied model. We define a suitable notion of a weighted first-order logic. Then we show that this weighted first-order logic and aperiodic polynomially ambiguous weighted automata have the same expressive power. Moreover, we obtain such equivalence results for suitable weighted sublogics and finitely ambiguous or unambiguous aperiodic weighted automata. Our results hold for general weight structures, including all semirings, average computations of costs, bounded lattices, and others.

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 languages, such as tree-languages did not work as smoothly: for instance W. Thomas showed that there are star-free tree languages that are counting. We show, instead, that investigating the same properties within the family of operator precedence languages leads to equivalences that perfectly match those on regular languages. The study of this old family of context-free languages has been recently resumed to enhance not only parsing (the original motivation of its inventor R. Floyd) but also to exploit their algebraic and logic properties. We have been able to reproduce the classic results of regular languages for this much larger class by going back to string languages rather than tree languages. Since operator precedence languages strictly include other classes of structured languages such as visibly pushdown languages, the same results given in this paper hold as trivial corollary for that family too.

Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. Büchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory. For example, certain acceptance conditions can be handled more efficiently than others by dedicated tools and algorithms. Furthermore, some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic omega-automata. However, properties cannot always be represented by automata with the desired acceptance condition and determinism. In this paper we study the problem of approximating linear-time properties by automata in a given class. Our approximation is based on preserving the language up to a user-defined precision given in terms of the size of the finite lasso representation of infinite executions that are preserved. We study the state complexity of different types of approximating automata, and provide constructions for the approximation within different automata classes, for example, for approximating a given automaton by one with a simpler acceptance condition.

Limit-average automata are weighted automata on infinite words that use average to aggregate the weights seen in infinite runs. We study approximate learning problems for limit-average automata in two settings: passive and active. In the passive learning case, we show that limit-average automata are not PAC-learnable as samples must be of exponential-size to provide (with good probability) enough details to learn an automaton. We also show that the problem of finding an automaton that fits a given sample is NP-complete. In the active learning case, we show that limit-average automata can be learned almost-exactly, i.e., we can learn in polynomial time an automaton that is consistent with the target automaton on almost all words. On the other hand, we show that the problem of learning an automaton that approximates the target automaton (with perhaps fewer states) is NP-complete. The abovementioned results are shown for the uniform distribution on words. We briefly discuss learning over different distributions.

We present an exponential-time algorithm approximating the minimal lookahead necessary to win an ω -regular delay game.

This paper investigates a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language \(L\) is REG-measurable if there exists an infinite sequence of regular languages that "converges" to \(L\). A language without REG-measurability has a complex shape in some sense so that it can not be (asymptotically) approximated by regular languages. We show that several context-free languages are REG-measurable (including languages with transcendental generating function and transcendental density, in particular), while a certain simple deterministic context-free language and the set of primitive words are REG-immeasurable in a strong sense.

In this work, we study the problem of supervisory control of discrete-event systems (DES) in the presence of attacks that tamper with inputs and outputs of the plant. We consider a very general system setup as we focus on both deterministic and nondeterministic plants that we model as finite state transducers (FSTs); this also covers the conventional approach to modeling DES as deterministic finite automata. Furthermore, we cover a wide class of attacks that can nondeterministically add, remove, or rewrite a sensing and/or actuation word to any word from predefined regular languages, and show how such attacks can be modeled by nondeterministic FSTs; we also present how the use of FSTs facilitates modeling realistic (and very complex) attacks, as well as provides the foundation for design of attack-resilient supervisory controllers. Specifically, we first consider the supervisory control problem for deterministic plants with attacks (i) only on their sensors, (ii) only on their actuators, and (iii) both on their sensors and actuators. For each case, we develop new conditions for controllability in the presence of attacks, as well as synthesizing algorithms to obtain FST-based description of such attack-resilient supervisors. A derived resilient controller provides a set of all safe control words that can keep the plant work desirably even in the presence of corrupted observation and/or if the control words are subjected to actuation attacks. Then, we extend the controllability theorems and the supervisor synthesizing algorithms to nondeterministic plants that satisfy a nonblocking condition. Finally, we illustrate applicability of our methodology on several examples and numerical case-studies.

We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of languages and their recognizing algebraic structures. Using the concept of anautomata presentation of T-algebras, we demonstrate that the task of learning a T-recognizable language can be reduced to learning an abstract form of algebraic automaton whose transitions are modeled by a functor. For the important case of adjoint automata, we devise a learning algorithm generalizing Angluin's L*. The algorithm is phrased in terms of categorically described extension steps; we provide for a termination and complexity analysis based on a dedicated notion of finiteness. Our framework applies to structures like omega-regular languages that were not within the scope of existing categorical accounts of automata learning. In addition, it yields new learning algorithms for several types of languages for which no such algorithms were previously known at all, including sorted languages, nominal languages with name binding, and cost functions.

Computer science class enrollments have rapidly risen in the past decade. With current class sizes, standard approaches to grading and providing personalized feedback are no longer possible and new techniques become both feasible and necessary. In this paper, we present the third version of Automata Tutor, a tool for helping teachers and students in large courses on automata and formal languages. The second version of Automata Tutor supported automatic grading and feedback for finite-automata constructions and has already been used by thousands of users in dozens of countries. This new version of Automata Tutor supports automated grading and feedback generation for a greatly extended variety of new problems, including problems that ask students to create regular expressions, context-free grammars, pushdown automata and Turing machines corresponding to a given description, and problems about converting between equivalent models - e.g., from regular expressions to nondeterministic finite automata. Moreover, for several problems, this new version also enables teachers and students to automatically generate new problem instances. We also present the results of a survey run on a class of 950 students, which shows very positive results about the usability and usefulness of the tool.