Related papers: Introducing Proof Tree Automata and Proof Tree Gra…
This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of…
This paper grew out of three tutorial lectures on automatic structures given by the first author at the Logic Colloquium 2007. We discuss variants of automatic structures related to several models of computation: word automata, tree…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
Parikh (tree) automata are an expressive and yet computationally well-behaved extension of finite automata -- they allow to increment a number of counters during their computations, which are finally tested by a semilinear constraint. In…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
Forest automata (FA) have recently been proposed as a tool for shape analysis of complex heap structures. FA encode sets of tree decompositions of heap graphs in the form of tuples of tree automata. In order to allow for representing…
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…
This paper presents a new approach to the solution of Probabilistic Risk Assessment (PRA) models using the combination of Reinforcement Learning (RL) and Graph Neural Networks (GNNs). The paper introduces and demonstrates the concept using…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…
Classical automata theory is far more capable of modeling complex digital systems than is widely acknowledged in the ``formal methods'' literature. This paper takes a second look at automata theory methods that were mostly developed in the…
We propose a sound and complete proof rule ProbTA for quantitative analysis of violation probability of probabilistic programs. Our approach extends the technique of trace abstraction with probability in the control-flow randomness style,…
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic. The clause selection heuristics in such systems are, however, often evaluating…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
Graph-Rewriting Automata (GRA) are an extension of Cellular Automata to a dynamic structure using local graph-rewriting rules. This work introduces linear algebra based tools that allow for a practical investigation of their behavior in…
The Graph Automata have been the paradigm in the expression of utilizing Graphs as a language. Matrix Graph grammars \cite{Pedro} are an algebratization of graph rewriting systems. Here we present the dual of this formalizm which some…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
This is a book on weighted tree automata. We present the basic definitions and some of the important results in a coherent form with full proofs. The concept of weighted tree automata is part of Automata Theory and it touches the area of…