Related papers: First-Order Quantification over Automata
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of…
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…
We study Parikh automata on finite and infinite words. First we establish some results for Parikh automata on finite words. Following, we present several definitions of Parikh automata on infinite words. We consider the deterministic as…
Since Edward Moore, finite automata theory has been inspired by physics, in particular by quantum complementarity. We review automaton complementarity, reversible automata and the connections to generalized urn models. Recent developments…
We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
We show how to compute efficiently with nominal sets over the total order symmetry, by developing a direct representation of such nominal sets and basic constructions thereon. In contrast to previous approaches, we work directly at the…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
Second-order quantifier elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of…
Dirac notation is widely used in quantum physics and quantum programming languages to define, compute and reason about quantum states. This paper considers Dirac notation from the perspective of automated reasoning. We prove two main…
Quotient is a basic operation of formal languages, which plays a key role in the construction of minimal deterministic finite automata (DFA) and the universal automata. In this paper, we extend this operation to formal power series and…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
Universal quantifiers occur frequently in proof obligations produced by program verifiers, for instance, to axiomatize uninterpreted functions and to express properties of arrays. SMT-based verifiers typically reason about them via…
Question answering (QA) systems are among the most important and rapidly developing research topics in natural language processing (NLP). A reason, therefore, is that a QA system allows humans to interact more naturally with a machine,…
Many methods for the verification of complex computer systems require the existence of a tractable mathematical abstraction of the system, often in the form of an automaton. In reality, however, such a model is hard to come up with, in…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Since the 1970s with the work of McNaughton, Papert and Sch\"utzenberger, a regular language is known to be definable in the first-order logic if and only if its syntactic monoid is aperiodic. This algebraic characterisation of a…
In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…
We consider two-variable first-order logic $\text{FO}^2$ and its quantifier alternation hierarchies over both finite and infinite words. Our main results are forbidden patterns for deterministic automata (finite words) and for Carton-Michel…