Skip to main content
Login | Suomeksi | På svenska | In English

Transitive Closure Logic and Multihead Automata with Nested Pebbles

Show full item record

Title: Transitive Closure Logic and Multihead Automata with Nested Pebbles
Author(s): Hirvonen, Minna
Contributor: University of Helsinki, Faculty of Science, none
Discipline: none
Degree program: Master's Programme in Mathematics and Statistics
Specialisation: Mathematics
Language: English
Acceptance year: 2020
Abstract:
Several extensions of first-order logic are studied in descriptive complexity theory. These extensions include transitive closure logic and deterministic transitive closure logic, which extend first-order logic with transitive closure operators. It is known that deterministic transitive closure logic captures the complexity class of the languages that are decidable by some deterministic Turing machine using a logarithmic amount of memory space. An analogous result holds for transitive closure logic and nondeterministic Turing machines. This thesis concerns the k-ary fragments of these two logics. In each k-ary fragment, the arities of transitive closure operators appearing in formulas are restricted to a nonzero natural number k. The expressivity of these fragments can be studied in terms of multihead finite automata. The type of automaton that we consider in this thesis is a two-way multihead automaton with nested pebbles. We look at the expressive power of multihead automata and the k-ary fragments of transitive closure logics in the class of finite structures called word models. We show that deterministic twoway k-head automata with nested pebbles have the same expressive power as first-order logic with k-ary deterministic transitive closure. For a corresponding result in the case of nondeterministic automata, we restrict to the positive fragment of k-ary transitive closure logic. The two theorems and their proofs are based on the article ’Automata with nested pebbles capture first-order logic with transitive closure’ by Joost Engelfriet and Hendrik Jan Hoogeboom. In the article, the results are proved in the case of trees. Since word models can be viewed as a special type of trees, the theorems considered in this thesis are a special case of a more general result.
Keyword(s): First-order logic transitive closure multihead automata pebbles word models


Files in this item

Files Size Format View
Hirvonen_Minna_Pro_gradu_2020.pdf 462.7Kb PDF

This item appears in the following Collection(s)

Show full item record