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  1. 6 Formalized Mathematics

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  1. 6 Trybulec M.

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  1. 2 2009

  2. 1 2008

  3. 3 2007

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1
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Labelled State Transition Systems

100%
Trybulec M.
Formalized Mathematics
|
2009
|
tom 17
|
nr 2
163-171
EN
This article introduces labelled state transition systems, where transitions may be labelled by words from a given alphabet. Reduction relations from [4] are used to define transitions between states, acceptance of words, and reachable states. Deterministic transition systems are also defined.
2
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String Rewriting Systems

100%
Trybulec M.
Formalized Mathematics
|
2007
|
tom 15
|
nr 3
121-126
EN
Basing on the definitions from [15], semi-Thue systems, Thue systems, and direct derivations are introduced. Next, the standard reduction relation is defined that, in turn, is used to introduce derivations using the theory from [1]. Finally, languages generated by rewriting systems are defined as all strings reachable from an initial word. This is followed by the introduction of the equivalence of semi-Thue systems with respect to the initial word.
3
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Regular Expression Quantifiers - at leastmOccurrences

100%
Trybulec M.
Formalized Mathematics
|
2008
|
tom 16
|
nr 1
29-33
EN
This is the second article on regular expression quantifiers. [4] introduced the quantifiers m to n occurrences and optional occurrence. In the sequel, the quantifiers: at least m occurrences and positive closure (at least 1 occurrence) are introduced. Notation and terminology were taken from [8], several properties of regular expressions from [7].MML identifier: FLANG 3, version: 7.8.05 4.89.993
4
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Regular Expression Quantifiers -mtonOccurrences

100%
Trybulec M.
Formalized Mathematics
|
2007
|
tom 15
|
nr 2
53-58
EN
This article includes proofs of several facts that are supplemental to the theorems proved in [10]. Next, it builds upon that theory to extend the framework for proving facts about formal languages in general and regular expression operators in particular. In this article, two quantifiers are defined and their properties are shown: m to n occurrences (or the union of a range of powers) and optional occurrence. Although optional occurrence is a special case of the previous operator (0 to 1 occurrences), it is often defined in regex applications as a separate operator - hence its explicit definition and properties in the article. Notation and terminology were taken from [13].
5
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Formal Languages - Concatenation and Closure

100%
Trybulec M.
Formalized Mathematics
|
2007
|
tom 15
|
nr 1
11-15
EN
Formal languages are introduced as subsets of the set of all 0-based finite sequences over a given set (the alphabet). Concatenation, the n-th power and closure are defined and their properties are shown. Finally, it is shown that the closure of the alphabet (understood here as the language of words of length 1) equals to the set of all words over that alphabet, and that the alphabet is the minimal set with this property. Notation and terminology were taken from [5] and [13]. MML identifier: FLANG 1, version: 7.8.04 4.81.962
6
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Equivalence of Deterministic and Nondeterministic Epsilon Automata

100%
Trybulec M.
Formalized Mathematics
|
2009
|
tom 17
|
nr 2
193-199
EN
Based on concepts introduced in [14], semiautomata and leftlanguages, automata and right-languages, and langauges accepted by automata are defined. The powerset construction is defined for transition systems, semiautomata and automata. Finally, the equivalence of deterministic and nondeterministic epsilon automata is shown.
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