"Algebraick\u00E9 vlastnosti substituc\u00ED na trajektori\u00EDch"@cs . . . . . . "Algebraic properties of substitution on trajectories"@en . "0304-3975" . "464563" . "1"^^ . "substitution on trajectories; algebra"@en . "Algebraic properties of substitution on trajectories" . "369" . "RIV/47813059:19240/06:#0001875!RIV09-MSM-19240___" . . "3"^^ . "NL - Nizozemsko" . "1" . . . "Rodriguez-Paton, Alfonso" . "[FB6812421B61]" . "RIV/47813059:19240/06:#0001875" . "Sos\u00EDk, Petr" . "Algebraic properties of substitution on trajectories"@en . . "19240" . "THEORETICAL COMPUTER SCIENCE" . "14"^^ . "Algebraic properties of substitution on trajectories" . . "Language operations on trajectories provide a generalization of many common operations such as concatenation, quotient, shuffle and others. A trajectory is a syntactical condition determining positions where an operation is applied. Besides their elegant language-theoretical properties, the operations on trajectories have been used to solve problems in coding theory, bio-informatics and concurrency theory. We focus on algebraic properties of substitution on trajectories. Their characterization in terms of language-theoretical properties of the associated sets of trajectories is given. The transitivity property is of particular interest. Unlike, e.g., shuffle on trajectories, in the case of substitution the transitive closure of a regular set of trajectories is again regular. This result has consequences in the above-mentioned application areas."@en . "Algebraick\u00E9 vlastnosti substituc\u00ED na trajektori\u00EDch"@cs . "Domaratzki, Michael" . . "S" . . "Language operations on trajectories provide a generalization of many common operations such as concatenation, quotient, shuffle and others. A trajectory is a syntactical condition determining positions where an operation is applied. Besides their elegant language-theoretical properties, the operations on trajectories have been used to solve problems in coding theory, bio-informatics and concurrency theory. We focus on algebraic properties of substitution on trajectories. Their characterization in terms of language-theoretical properties of the associated sets of trajectories is given. The transitivity property is of particular interest. Unlike, e.g., shuffle on trajectories, in the case of substitution the transitive closure of a regular set of trajectories is again regular. This result has consequences in the above-mentioned application areas." . . "Operace s form\u00E1ln\u00EDmi jazyky na trajektori\u00EDch jsou r\u00E1mcem zobec\u0148uj\u00EDc\u00EDm \u0159adu b\u011B\u017En\u00FDch jazykov\u00FDch operac\u00ED jako z\u0159et\u011Bzen\u00ED, kvocient, vsouv\u00E1n\u00ED a dal\u0161\u00ED. Zde se zam\u011B\u0159ujeme na algebraick\u00E9 vlastnosti substituc\u00ED na trajektori\u00EDch. Zvl\u00E1\u0161t\u011B zaj\u00EDmav\u00E1 je tranzitivita - na rozd\u00EDl od jin\u00FDch obdobn\u00FDch operac\u00ED je uzav\u0159en\u00E1 vzhledem ke t\u0159\u00EDd\u011B regul\u00E1rn\u00EDch jazyk\u016F."@cs .