Related papers: Distributed Graph Automata and Verification of Dis…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…
We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of…
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…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not…
We investigate the decidability of the emptiness problem for three classes of distributed automata. These devices operate on finite directed graphs, acting as networks of identical finite-state machines that communicate in an infinite…
Esparza and Reiter have recently conducted a systematic comparative study of weak asynchronous models of distributed computing, in which a network of identical finite-state machines acts cooperatively to decide properties of the network's…
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…
Engelfriet and Vereijken have shown that linear graph grammars based on hyperedge replacement generate graph languages that can be considered as interpretations of regular string languages over typed symbols. In this paper we show that…
In this paper we survey some surprising connections between group theory, the theory of automata and formal languages, the theory of ends, infinite games of perfect information, and monadic second-order logic.
We establish the equivalence between a class of asynchronous distributed automata and a small fragment of least fixpoint logic, when restricted to finite directed graphs. More specifically, the logic we consider is (a variant of) the…
Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization…
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…
The work presents some new algorithms realized recently in the package TESTAS. They decide whether or not deterministic finite automaton (DFA) is synchronizing, several procedures find relatively short synchronizing words and a…
We consider distributed model-checking of Monadic Second-Order logic (MSO) on graphs which constitute the topology of communication networks. The graph is thus both the structure being checked and the system on which the distributed…
We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader).…
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…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…