A Landscape of Logics for Finite Unordered Unranked Trees
نویسنده
چکیده
In this paper we study a large number of logics to define languages of unordered unranked trees and compare their expressive power. Generally speaking, the logics we consider stem from three non-disjoint areas: logics related to automata theory, logics discussed in descriptive complexity theory, and second-order logics. The basic logic from automata theory is monadic second-order logic. Two extensions of this logic will also be discussed. From the area of descriptive complexity theory we consider
منابع مشابه
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Further...
متن کاملA Note on Recognizable Sets of Unranked and Unordered Trees
Recognizable sets of unranked, unordered trees have been introduced in Courcelle [C89] in a Myhill-Nerode [N58] style of inverse homomorphisms of suitable finite magmas. This is equivalent of being the the union of some congruence classes of a congruence of finite index. We will add to the well-known concept of regular tree grammars a handling of nodes labeled with ǫ. With this rather unconvent...
متن کاملAutomata and Logics for Unranked and Unordered Trees
In this paper, we consider the monadic second order logic (MSO) and two of its extensions, namely Counting MSO (CMSO) and Presburger MSO (PMSO), interpreted over unranked and unordered trees. We survey classes of tree automata introduced for the logics PMSO and CMSO as well as other related formalisms; we gather results from the literature and sometimes clarify or fill the remaining gaps betwee...
متن کاملFinite Automata on Unranked and Unordered DAGs Extented Version
We introduce linear expressions for unrestricted dags (directed acyclic graphs) and finite deterministic and nondeterministic automata operating on them. Those dag automata are a conservative extension of the Tu,u-automata of Courcelle on unranked, unordered trees and forests. Several examples of dag languages acceptable and not acceptable by dag automata and some closure properties are given.
متن کاملA pr 2 00 9 TWO - WAY UNARY TEMPORAL LOGIC OVER TREES
We consider a temporal logic EF + F −1 for unranked, unordered finite trees. The logic has two operators: EFϕ, which says " in some proper descendant ϕ holds " , and F −1 ϕ, which says " in some proper ancestor ϕ holds ". We present an algorithm for deciding if a regular language of unranked finite trees can be expressed in EF + F −1. The algorithm uses a characterization expressed in terms of ...
متن کامل