{"id":{"repo_id":"usf","oai_identifier":"oai:digitalcommons.usf.edu:etd-1216"},"canonical_url":"https://search.dev.ndltd.org/etd/usf/oai:digitalcommons.usf.edu:etd-1216","repository":{"repo_id":"usf","name":"University of South Florida","base_url":"https://digitalcommons.usf.edu/do/oai/"},"display":{"title":"Transducer dynamics","abstract":"Transducers are finite state automata with an output. In this thesis, we attempt to classify sequences that can be constructed by iteratively applying a transducer to a given word. We begin exploring this problem by considering sequences of words that can be produced by iterative application of a transducer to a given input word, i.e., identifying sequences of words of the form w, t(w), t²(w), . . . We call such sequences transducer recognizable. Also we introduce the notion of \"recognition of a sequence in context\", which captures the possibility of concatenating prefix and suffix words to each word in the sequence, so a given sequence of words becomes transducer recognizable. It turns out that all finite and periodic sequences of words of equal length are transducer recognizable. We also show how to construct a deterministic transducer with the least number of states recognizing a given sequence. To each transducer t we associate a two-dimensional language L²(t) consisting of blocks of symbols in the following way. The first row, w, of each block is in the input language of t, the second row is a word that t outputs on input w. Inductively, every subsequent row is a word outputted by the transducer when its preceding row is read as an input. We show a relationship of the entropy values of these two-dimensional languages to the entropy values of the one-dimensional languages that appear as input languages for finite state transducers.","abstract_html":"Transducers are finite state automata with an output. In this thesis, we attempt to classify sequences that can be constructed by iteratively applying a transducer to a given word. We begin exploring this problem by considering sequences of words that can be produced by iterative application of a transducer to a given input word, i.e., identifying sequences of words of the form w, t(w), t²(w), . . . We call such sequences transducer recognizable. Also we introduce the notion of "recognition of a sequence in context", which captures the possibility of concatenating prefix and suffix words to each word in the sequence, so a given sequence of words becomes transducer recognizable. It turns out that all finite and periodic sequences of words of equal length are transducer recognizable. We also show how to construct a deterministic transducer with the least number of states recognizing a given sequence. To each transducer t we associate a two-dimensional language L²(t) consisting of blocks of symbols in the following way. The first row, w, of each block is in the input language of t, the second row is a word that t outputs on input w. Inductively, every subsequent row is a word outputted by the transducer when its preceding row is read as an input. We show a relationship of the entropy values of these two-dimensional languages to the entropy values of the one-dimensional languages that appear as input languages for finite state transducers.","abstract_has_math":false,"creators":["Dolzhenko, Egor"],"institution":"Digital Commons @ University of South Florida","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2007,"date_issued":"2007-12-14T08:00:00Z","date_published":"2007-12-14T08:00:00Z","updated_at":"2026-07-24T05:42:29Z","subjects":["Sequences of Words","Finite State Automata with Output","Entropy","Picture Languages","Local Languages","American Studies","Arts and Humanities"],"languages":[],"rights":["default"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.usf.edu/etd/217","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Dolzhenko, Egor"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-12-14T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Digital Commons @ University of South Florida"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Sequences of Words","Finite State Automata with Output","Entropy","Picture Languages","Local Languages","American Studies","Arts and Humanities"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["default"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.usf.edu/etd/217","https://digitalcommons.usf.edu/context/etd/article/1216/viewcontent/etd__217.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Transducers are finite state automata with an output. In this thesis, we attempt to classify sequences that can be constructed by iteratively applying a transducer to a given word. We begin exploring this problem by considering sequences of words that can be produced by iterative application of a transducer to a given input word, i.e., identifying sequences of words of the form w, t(w), t²(w), . . . We call such sequences transducer recognizable. Also we introduce the notion of \"recognition of a sequence in context\", which captures the possibility of concatenating prefix and suffix words to each word in the sequence, so a given sequence of words becomes transducer recognizable. It turns out that all finite and periodic sequences of words of equal length are transducer recognizable. We also show how to construct a deterministic transducer with the least number of states recognizing a given sequence. To each transducer t we associate a two-dimensional language L²(t) consisting of blocks of symbols in the following way. The first row, w, of each block is in the input language of t, the second row is a word that t outputs on input w. Inductively, every subsequent row is a word outputted by the transducer when its preceding row is read as an input. We show a relationship of the entropy values of these two-dimensional languages to the entropy values of the one-dimensional languages that appear as input languages for finite state transducers."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:source","label":"Dc Source","values":["USF Tampa Graduate Theses and Dissertations"]},{"key":"dc:title","label":"Title","values":["Transducer dynamics"]}]}],"canonical_facts":{"dc:creator":["Dolzhenko, Egor"],"dc:date":["2007-12-14T08:00:00Z"],"dc:description":["Transducers are finite state automata with an output. In this thesis, we attempt to classify sequences that can be constructed by iteratively applying a transducer to a given word. We begin exploring this problem by considering sequences of words that can be produced by iterative application of a transducer to a given input word, i.e., identifying sequences of words of the form w, t(w), t²(w), . . . We call such sequences transducer recognizable. Also we introduce the notion of \"recognition of a sequence in context\", which captures the possibility of concatenating prefix and suffix words to each word in the sequence, so a given sequence of words becomes transducer recognizable. It turns out that all finite and periodic sequences of words of equal length are transducer recognizable. We also show how to construct a deterministic transducer with the least number of states recognizing a given sequence. To each transducer t we associate a two-dimensional language L²(t) consisting of blocks of symbols in the following way. The first row, w, of each block is in the input language of t, the second row is a word that t outputs on input w. Inductively, every subsequent row is a word outputted by the transducer when its preceding row is read as an input. We show a relationship of the entropy values of these two-dimensional languages to the entropy values of the one-dimensional languages that appear as input languages for finite state transducers."],"dc:format":["application/pdf"],"dc:identifier":["https://digitalcommons.usf.edu/etd/217","https://digitalcommons.usf.edu/context/etd/article/1216/viewcontent/etd__217.pdf"],"dc:publisher":["Digital Commons @ University of South Florida"],"dc:rights":["default"],"dc:source":["USF Tampa Graduate Theses and Dissertations"],"dc:subject":["Sequences of Words","Finite State Automata with Output","Entropy","Picture Languages","Local Languages","American Studies","Arts and Humanities"],"dc:title":["Transducer dynamics"],"dc:type":["thesis"]},"updated_at":"2026-07-24T05:42:29Z"}