Related papers: Subshifts, Languages and Logic
We study the Monadic Second Order (MSO) Hierarchy over colourings of the discrete plane, and draw links between classes of formula and classes of subshifts. We give a characterization of existential MSO in terms of projections of tilings,…
We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In…
We define sets of coulourings of the infinite discrete plane using monadic second order (MSO) formulas. We determine the complexity of deciding whether such a formula defines a subshift, parametrized on the quantifier alternation complexity…
Monadic Second-Order Logic (MSO) extends First-Order Logic (FO) with variables ranging over sets and quantifications over those variables. We introduce and study Monadic Tree Logic (MTL), a fragment of MSO interpreted on infinite-tree…
Traditionally a tiling is defined with a finite number of finite forbidden patterns. We can generalize this notion considering any set of patterns. Generalized tilings defined in this way can be studied with a dynamical point of view,…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the…
Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary…
MSO transductions are binary relations between structures which are defined using monadic second-order logic. MSO transductions form a category, since they are closed under composition. We show that many notions from language theory, such…
We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic, automata-theoretic and machine-independent…
We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present…
Second-order transitive-closure logic, SO(TC), is an expressive declarative language that captures the complexity class PSPACE. Already its monadic fragment, MSO(TC), allows the expression of various NP-hard and even PSPACE-hard problems in…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
We investigate the extension of Monadic Second Order logic, interpreted over infinite words and trees, with generalized "for almost all" quantifiers interpreted using the notions of Baire category and Lebesgue measure.
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…
Expansions of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N} ; < \rangle$ have been a fertile and active area of research ever since the publication of the seminal papers of B\"uchi and Elgot & Rabin on the…
We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers,…
We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for omega-languages: Sigma_2, FO^2, the intersection of FO^2 and Sigma_2, and Delta_2 (and…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…
We study on which classes of graphs first-order logic (FO) and monadic second-order logic (MSO) have the same expressive power. We show that for all classes C of graphs that are closed under taking subgraphs, FO and MSO have the same…