Related papers: Certifying DFA Bounds for Recognition and Separati…
We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader).…
A cryptarithm is a mathematical puzzle where given an arithmetic equation written with letters rather than numerals, a player must discover an assignment of numerals on letters that makes the equation hold true. In this paper, we propose a…
In this paper we revisit Safra's determinization constructions for automata on infinite words. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Determinization is used in…
We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that…
As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact…
We investigate a famous decision problem in automata theory: separation. Given a class of language C, the separation problem for C takes as input two regular languages and asks whether there exists a third one which belongs to C, includes…
It is well known that computing a minimum DFA consistent with a given set of positive and negative examples is NP-hard. Previous work has identified conditions on the input sample under which the problem becomes tractable or remains hard.…
An essential element of any verification technique is that of identifying and communicating to the user, system behaviour which leads to a deviation from the expected behaviour. Such behaviours are typically made available as long traces of…
It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that…
The identification of deterministic finite automata (DFAs) from labeled examples is a cornerstone of automata learning, yet traditional methods focus on learning monolithic DFAs, which often yield a large DFA lacking simplicity and…
In this paper, we investigate the computational and verification power of bounded-error postselecting realtime probabilistic finite state automata (PostPFAs). We show that PostPFAs using rational-valued transitions can do different variants…
Minimal deterministic finite automata (DFAs) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the…
In model-based reinforcement learning for safety-critical control systems, it is important to formally certify system properties (e.g., safety, stability) under the learned controller. However, as existing methods typically apply formal…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. $\textit{Complement:}$ There is a language $L$ recognised by an $n$-state UFA such…
We show the surprising result that the cutpoint isolation problem is decidable for Probabilistic Finite Automata (PFA) where input words are taken from a letter-bounded context-free language. A context-free language $\mathcal{L}$ is…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
Neural network (NN) controllers achieve strong empirical performance on nonlinear dynamical systems, yet deploying them in safety-critical settings requires robustness to disturbances and uncertainty. We present a method for jointly…
We present an algorithm for regular expression parsing and submatch extraction based on tagged deterministic finite automata. The algorithm works with different disambiguation policies. We give detailed pseudocode for the algorithm,…
We work on the task of automatically designing a treatment plan from the findings included in the medical certificate written by the dentist. To develop an artificial intelligence system that deals with free-form certificates written by…