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Transitive Closure Logic and Multihead Automata with Nested Pebbles

Show simple item record 2020-05-27T05:07:31Z 2020-05-27T05:07:31Z 2020-05-27
dc.title Transitive Closure Logic and Multihead Automata with Nested Pebbles en
ethesis.discipline none und
ethesis.department none und
ethesis.faculty Matemaattis-luonnontieteellinen tiedekunta fi
ethesis.faculty Faculty of Science en
ethesis.faculty Matematisk-naturvetenskapliga fakulteten sv
ethesis.faculty.URI Helsingin yliopisto fi University of Helsinki en Helsingfors universitet sv
dct.creator Hirvonen, Minna
dct.issued 2020
dct.language.ISO639-2 eng
dct.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. en
dct.subject First-order logic
dct.subject transitive closure
dct.subject multihead automata
dct.subject pebbles
dct.subject word models
dct.language en
ethesis.isPublicationLicenseAccepted true
ethesis.language English en
ethesis.language englanti fi
ethesis.language engelska sv
ethesis.thesistype pro gradu -tutkielmat fi
ethesis.thesistype master's thesis en
ethesis.thesistype pro gradu-avhandlingar sv
dct.identifier.ethesis E-thesisID:7c2a4bc7-8e14-49e0-b0bb-1f5e60412526
dct.identifier.urn URN:NBN:fi:hulib-202005272339
dc.type.dcmitype Text
ethesis.facultystudyline Matematiikka fi
ethesis.facultystudyline Mathematics en
ethesis.facultystudyline Matematik sv
ethesis.mastersdegreeprogram Matematiikan ja tilastotieteen maisteriohjelma fi
ethesis.mastersdegreeprogram Master's Programme in Mathematics and Statistics en
ethesis.mastersdegreeprogram Magisterprogrammet i matematik och statistik sv

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