English
Related papers

Related papers: Constant time testability of first-order logic wit…

200 papers

In this paper, we analyze timed systems with data structures, using a rich interplay of logic and properties of graphs. We start by describing behaviors of timed systems using graphs with timing constraints. Such a graph is called…

Logic in Computer Science · Computer Science 2019-04-30 S. Akshay , Paul Gastin , Vincent Juge , Shankara Narayanan Krishna

One of the most famous algorithmic meta-theorems states that every graph property that can be defined by a sentence in counting monadic second order logic (CMSOL) can be checked in linear time for graphs of bounded treewidth, which is known…

Logic in Computer Science · Computer Science 2015-09-29 Lars Jaffke , Hans L. Bodlaender

It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 ... x_k \#y…

Logic in Computer Science · Computer Science 2023-07-06 Jan Dreier , Daniel Mock , Peter Rossmanith

Distributed networks are prone to errors so verifying their output is critical. Hence, we develop LOCAL certification protocols for graph properties in which nodes are given certificates that allow them to check whether their network as a…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-03-16 Linda Cook , Eun Jung Kim , Tomáš Masařík

Our starting point is the observation that if graphs in a class C have low descriptive complexity in first order logic, then the isomorphism problem for C is solvable by a fast parallel algorithm (essentially, by a simple combinatorial…

Computational Complexity · Computer Science 2007-05-23 Martin Grohe , Oleg Verbitsky

Possibly the most famous algorithmic meta-theorem is Courcelle's theorem, which states that all MSO-expressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time's dependence on…

Data Structures and Algorithms · Computer Science 2009-11-05 Michael Lampis

The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-10-18 Nicolas Bousquet , Laurent Feuilloley , Théo Pierron

In this paper we extend and prove in detail the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and J.A.…

Logic in Computer Science · Computer Science 2015-07-01 Tomer Kotek , Johann A. Makowsky

We study the classification problems over string data for hypotheses specified by formulas of monadic second-order logic MSO. The goal is to design learning algorithms that run in time polynomial in the size of the training set,…

Machine Learning · Computer Science 2017-08-29 Martin Grohe , Christof Löding , Martin Ritzert

We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…

Data Structures and Algorithms · Computer Science 2022-11-07 Fedor V. Fomin , Petr A. Golovach , Ignasi Sau , Giannos Stamoulis , Dimitrios M. Thilikos

We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in…

Discrete Mathematics · Computer Science 2021-10-12 Zdeněk Dvořák

The main focus of this paper is on bisimulation-invariant MSO, and more particularly on giving a novel model-theoretic approach to it. In model theory, a model companion of a theory is a first-order description of the class of models in…

Logic · Mathematics 2016-05-04 Silvio Ghilardi , Samuel J. van Gool

Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…

Logic in Computer Science · Computer Science 2025-01-09 Max Bannach , Markus Hecher

We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…

Data Structures and Algorithms · Computer Science 2018-09-19 Ashish Chiplunkar , Michael Kapralov , Sanjeev Khanna , Aida Mousavifar , Yuval Peres

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…

Logic in Computer Science · Computer Science 2015-07-01 Achim Blumensath , Bruno Courcelle

We introduce a logic called distance neighborhood logic with acyclicity and connectivity constraints ($\mathsf{A\&C~DN}$ for short) which extends existential $\mathsf{MSO_1}$ with predicates for querying neighborhoods of vertex sets and for…

Data Structures and Algorithms · Computer Science 2022-12-09 Benjamin Bergougnoux , Jan Dreier , Lars Jaffke

We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, such as reachability and full linear temporal logic. The main idea is that we monitor each simulation run on the…

Logic in Computer Science · Computer Science 2016-03-04 Przemysław Daca , Thomas A. Henzinger , Jan Křetínský , Tatjana Petrov

We study the question of local testability of low (constant) degree functions from a product domain $S_1 \times \dots \times {S}_n$ to a field $\mathbb{F}$, where ${S_i} \subseteq \mathbb{F}$ can be arbitrary constant sized sets. We show…

Computational Complexity · Computer Science 2024-11-12 Prashanth Amireddy , Srikanth Srinivasan , Madhu Sudan

In this work we provide algorithmic solutions to five fundamental problems concerning the verification, synthesis and correction of concurrent systems that can be modeled by bounded p/t-nets. We express concurrency via partial orders and…

Logic in Computer Science · Computer Science 2014-02-14 Mateus de Oliveira Oliveira

One of the most important algorithmic meta-theorems is a famous result by Courcelle, which states that any graph problem definable in monadic second-order logic with edge-set quantifications (i.e., MSO2 model-checking) is decidable in…

Logic in Computer Science · Computer Science 2012-06-25 Robert Ganian , Petr Hliněný , Alexander Langer , Jan Obdržálek , Peter Rossmanith , Somnath Sikdar