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We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
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…
Recursion is a prominent feature of human language, and fundamentally challenging for self-attention due to the lack of an explicit recursive-state tracking mechanism. Consequently, Transformer language models poorly capture long-tail…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
Recently we proposed relative observability for supervisory control of discrete-event systems under partial observation. Relative observability is closed under set unions and hence there exists the supremal relatively observable sublanguage…
Nonuniform families of polynomial-size finite automata and pushdown automata respectively have strong connections to nonuniform-NL and nonuniform-LOGCFL. We examine the behaviors of unambiguous and co-nondeterministic computations produced…
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…
Slicing is a program analysis technique originally developed for imperative languages. It facilitates understanding of data flow and debugging. This paper discusses slicing of Constraint Logic Programs. Constraint Logic Programming (CLP) is…
Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for…
The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently.…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
For general input automata, there exist regular constraint languages such that asking if a given input automaton admits a synchronizing word in the constraint language is PSPACE-complete or NP-complete. Here, we investigate this problem for…
Abstract machines for the strong evaluation of lambda-terms (that is, under abstractions) are a mostly neglected topic, despite their use in the implementation of proof assistants and higher-order logic programming languages. This paper…
In the static analysis of functional programs, pushdown flow analysis and abstract garbage collection skirt just inside the boundaries of soundness and decidability. Alone, each method reduces analysis times and boosts precision by orders…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…
While transformer models exhibit strong capabilities on linguistic tasks, their complex architectures make them difficult to interpret. Recent work has aimed to reverse engineer transformer models into human-readable representations called…
We introduce an operator on classes of regular languages, the star-free closure. Our motivation is to generalize standard results of automata theory within a unified framework. Given an arbitrary input class $C$, the star-free closure…