Related papers: Pecan: An Automated Theorem Prover for Automatic S…
Given an $\omega$-automaton and a set of substitutions, we look at which accepted words can also be defined through these substitutions, and in particular if there is at least one. We introduce a method using desubstitution of…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Verifying partial (i.e., termination-insensitive) equivalence of programs has significant practical applications in software development and education. Conventional equivalence verifiers typically rely on a combination of given relational…
We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different…
We study methods for automated parsing of informal mathematical expressions into formal ones, a main prerequisite for deep computer understanding of informal mathematical texts. We propose a context-based parsing approach that combines…
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…
Abelian complexity of a word $\mathbf{u}$ is a function that counts the number of pairwise non-abelian-equivalent factors of $\mathbf{u}$ of length $n$. We prove that for any $c$-balanced Parry word $\mathbf{u}$, the values of the abelian…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…
Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree…
The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and…
We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams…
Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
In Machine-Assisted Theorem Proving, a theorem proving agent searches for a sequence of expressions and tactics that can prove a conjecture in a proof assistant. In this work, we introduce several novel concepts and capabilities to address…
Many combinatorial sequences (for example, the Catalan and Motzkin numbers) may be expressed as the constant term of $P(x)^k Q(x)$, for some Laurent polynomials $P(x)$ and $Q(x)$ in the variable $x$ with integer coefficients. Denoting such…
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
We introduce presheaf automata as a generalisation of different variants of higher-dimensional automata and other automata-like formalisms, including Petri nets and vector addition systems. We develop the foundations of a language theory…
This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…
Several approaches exist to data-mining big corpora of formal proofs. Some of these approaches are based on statistical machine learning, and some -- on theory exploration. However, most are developed for either untyped or simply-typed…