"C\u00EDlem projektu bylo studovat modely zalo\u017Een\u00E9 na bezkontextov\u00FDch gramatik\u00E1ch a automatech. Jejich nov\u011B popsan\u00E9 vlastnosti byly prezentov\u00E1ny na 4 ve\u0159ejn\u00FDch odborn\u00FDch semin\u00E1\u0159\u00EDch a publikov\u00E1ny ve 4 mezin\u00E1rodn\u00EDch \u010Dasopisech a na n\u011Bkolika konferenc\u00EDch."@cs . . "formal language theory; primitive words; grammars; automata"@en . "2010-01-01+01:00"^^ . . . . . . "2011-03-07+01:00"^^ . "The planned research will focus on the study of context-free languages and pushdown automata and their applications. To understand the structure of formal languages is a helpful tool to study their combinatorial properties. One of the subjects of this research is the problem of primitive words. A word is called primitive if it is not a power of another word. A widely known conjecture of P. D\u00F6m\u00F6si, M. Ito, and S. Horv\u00E1th states that the language Q of all primitive words over an alphabet with several letters is not context-free. A number of recent papers investigated this well-known conjecture which is still open. We intend to continue our investigations on small context-free grammars generating primitive words. On the other hand, using the fact that a homomorphic map of a nonprimitive word is also nonprimitive, we also plan to study whether or not Q has a real Chomsky-Sch\u00FCtzenberger-Stanley type homomorphic characterization. By our hope, these investigations may lead to prove or disprove our conjectur"@en . . "We accomplished the main project goal to study context-free grammars and automata. The original results about their properties were presented at 4 public seminars and published in 4 international journals and several conferences."@en . . "Pl\u00E1novan\u00FD v\u00FDzkum se zam\u011B\u0159\u00ED na studium bezkontextov\u00FDch jazyk\u016F a z\u00E1sobn\u00EDkov\u00FDch automat\u016F a jejich aplikac\u00ED. Pro hlub\u0161\u00ED pochopen\u00ED struktur form\u00E1ln\u00EDch jazyk\u016F je n\u00E1pomocn\u00E9 studovat jejich kombinatorick\u00E9 vlastnosti. Jedn\u00EDm z p\u0159edm\u011Bt\u016F v\u00FDzkumu je probl\u00E9m primitivn\u00EDch slov. Slovo naz\u00FDv\u00E1me primitivn\u00ED, pokud nen\u00ED mocninou jin\u00E9ho slova. P. D\u00F6m\u00F6si, M. Ito a S. Horv\u00E1th prezentovali domn\u011Bnku, \u017Ee jazyk v\u0161ech primitivn\u00EDch slov nad abecedou s n\u011Bkolika symboly, Q, nen\u00ED bezkontextov\u00FD. Ned\u00E1vno publikovan\u00E9 \u010Dl\u00E1nky se st\u00E1le zab\u00FDvaj\u00ED t\u00EDmto proslul\u00FDm dohadem, kter\u00FD je st\u00E1le otev\u0159en\u00FDm probl\u00E9mem. Pl\u00E1nujeme d\u00E1le rozv\u00EDjet toto zkoum\u00E1n\u00ED se zam\u011B\u0159en\u00EDm na mal\u00E9 bezkontextov\u00E9 gramatiky generuj\u00EDc\u00ED primitivn\u00ED slova. Na druhou stranu, vezmeme-li v \u00FAvahu, \u017Ee homomorfick\u00FD obraz neprimitivn\u00EDho slova je tak\u00E9 neprimitivn\u00ED, budeme tak\u00E9 studovat, zda je Q skute\u010Dnou homomorfickou charakterizac\u00ED Chomsky-Sch\u00FCtzenberger-Stanleyho typu. Douf\u00E1me, \u017Ee toto zkoum\u00E1n\u00ED povede na d\u016Fkaz platnosti \u010Di neplatnosti p\u0159edchoz\u00ED domn\u011Bnky a otev\u0159en\u00E9ho probl\u00E9mu. D\u00E1le by" . "2011-12-31+01:00"^^ . "Bezkontextov\u00E9 gramatiky a z\u00E1sobn\u00EDkov\u00E9 automaty" . . "formal language theory" . "8"^^ . . "8"^^ . " primitive words" . . . . "1"^^ . " grammars" . . . "0"^^ . "0"^^ . "MEB041003" . "Context-free languages and pushdown automata"@en . . . "http://www.isvav.cz/projectDetail.do?rowId=MEB041003"^^ . . "2012-07-12+02:00"^^ .