On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection - Archive ouverte HAL Access content directly
Conference Papers Year : 2016

## On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection

(1) , (1) , (1) , (1) , (1)
1
Rafaela Bastos
• Function : Author
• PersonId : 1022728
Sabine Broda
• Function : Author
• PersonId : 1022729
António Machiavelo
• Function : Author
• PersonId : 1022730
Nelma Moreira
• Function : Author
• PersonId : 1022731
Rogério Reis
• Function : Author
• PersonId : 1022732

#### Abstract

Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of $2^{O(n)}$ for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of $(1.056 +o(1))^n$ for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case.

#### Domains

Computer Science [cs]
Loading...

### Dates and versions

hal-01633952 , version 1 (13-11-2017)

### Licence

Attribution - CC BY 4.0

### Identifiers

• HAL Id : hal-01633952 , version 1
• DOI :

### Cite

Rafaela Bastos, Sabine Broda, António Machiavelo, Nelma Moreira, Rogério Reis. On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection. 18th International Workshop on Descriptional Complexity of Formal Systems (DCFS), Jul 2016, Bucharest, Romania. pp.45-59, ⟨10.1007/978-3-319-41114-9_4⟩. ⟨hal-01633952⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

50 View
77 Download

### Share

Gmail Facebook Twitter LinkedIn More