Implementation of State Elimination Using Heuristics

1. Implementation of State Elimination UsingHeuristics Author: Jae-HeeAhn, Yo-Sub Han Publisher: CIAA 2009 Presenter: Li-Hsien, Hsu Data: 5/9/2012

2. Introduction

3. Introduction

4. Introduction The size of a regular expression from state elimination depends on the state removal sequence. 2 -> 4 4 -> 2

5. Heuristics for State Elimination • The Decomposition Heuristic • vertical decomposition • horizontal decomposition • The State Weight Heuristic

6. Vertical Decomposition • Definition 1. We define a state q in an FA A to be a bridge state if it satisfies the following conditions: 1. State q is neither a start nor a final state. 2. For each string w ∈ L(A), its path in A must pass through q at least once. 3. State q is not in any cycle except for the self-loop.

7. Vertical Decomposition

8. Horizontal Decomposition • For horizontal chopping of a given FA A = (Q,Σ, δ, s, f), we have to identify subautomataof A such that all subautomata are disjoint from each other except s and f.

9. The State Weight Heuristic

10. The State Weight Heuristic In = 1 Out = 2 (1*2)+(1*1+1*1)+5*(1*2) = 14

11. C-I Eliminate states in order. • C-II Using VC & HC, and eliminate States in order. • C-III Using SWH only once. • C-IV Using VC & HC, and eliminate States with SWH only once. • C-V Using SWH in every steps. • C-VI Using VC & HC, and eliminate States with SWH in every steps.