Related papers: Distributed Graph 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…
In this work we introduce new generalised quantifiers which allow us to express the Rabin-Mostowski index of automata. Our main results study expressive power and decidability of the monadic second-order (MSO) logic extended with these…
We prove that the isomorphism of scattered tree automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders are undecidable. For the existence of automatic automorphisms of word automatic…
We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in…
We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…
Semantic representations in the form of directed acyclic graphs (DAGs) have been introduced in recent years, and to model them, we need probabilistic models of DAGs. One model that has attracted some attention is the DAG automaton, but it…
We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving…
Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a_0 b_0 a_1 b_1 ... a_n b_n of even length over D can be viewed as a directed graph G_w whose vertices are the symbols that appear in w, and the…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for strict and non-strict cut-points of polynomially ambiguous…
We propose a new extension of higher-order pushdown automata, which allows to use an infinite alphabet. The new automata recognize languages of data words (instead of normal words), which beside each its letter from a finite alphabet have a…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
We explore language semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural semantics for probabilistic automata with nondeterminism. For both choices, we show that…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for…
We give a characterization of the sets of graphs that are both definable in Counting Monadic Second Order Logic (CMSO) and context-free, i.e., least solutions of Hyperedge-Replacement (HR) grammars introduced by Courcelle and Engelfriet. We…