## Simple-regular expressions and languages (2005)

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Venue: | In Proceedings of DCFS’05, 146–157 |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Han05simple-regularexpressions,

author = {Yo-sub Han and Derick Wood},

title = {Simple-regular expressions and languages},

booktitle = {In Proceedings of DCFS’05, 146–157},

year = {2005}

}

### OpenURL

### Abstract

We define simple-regular expressions and languages. Simple-regular languages provide a necessary condition for a language to be outfix-free. We design algorithms that compute simple-regular languages from finite-state automata. Furthermore, we investigate the complexity blowup from a given finite-state automaton to its simple-regular language automaton and show that there is an exponential blowup. In addition, we present a finite-state automata construction for simple-regular expressions based on state expansion. 1

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Citation Context ...ters on transitions, then A is an FA and if we only allow strings, then A is a generalized automaton [4, 5]. Since the strongly connected components of a directed graph can be computed in linear time =-=[1]-=-, we can identify all orbits of A in linear time in |A|. Once we identify orbits, then we compute all simple paths for each pair of an entry state and a gate state. 3.3 Computing all simple paths We d... |

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Citation Context ...based on state expansion. 1 Introduction It is well known that the family of languages specified by finite-state automata (FAs) is the same as the family of languages described by regular expressions =-=[13]-=-. It can be proved by showing that we can construct FAs from regular expressions and that we can construct regular expressions from FAs. Additionally, some automata constructions preserve the structur... |

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Citation Context ...ince p is a simple path only one bit in io must be 1 and the other bits must be 0. We search for the bit with 1. We notice that bit operations (for example, shift, and, or and not) take constant time =-=[15]-=-. We use binary search method to find the bit with 1 from io = i1i2 · · · ik using these bit operations. Assume that k is even. We shift i1i2 · · · ik to the left by k/2 and append a k/2 number of 0s ... |

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Citation Context ...ession E, then |S(E)| = O(|E|) by Definition 1. It leads us to consider the case when A preserves the structural properties of the corresponding regular expression. For example, the Thompson automata =-=[17]-=- are a proper subfamily of FAs although they represent all regular languages. Theorem 3. Given a Thompson automaton AT, we can compute the corresponding Thompson automaton A ′ T such that L(A′ T ) is ... |

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Citation Context ...h that each string is accepted by a simple path in A. 3.2 Simple-regular languages from finite-state automata We define a path to be simple if it does not have a cycle in A. Brüggemann-Klein and Wood =-=[2]-=- defined the orbit of a state q and its gate states to characterize one-unambiguous regular languages. The orbit O(q) of q in A is the strongly connected component of q; that is, it is the set of stat... |

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Citation Context ...pressions from FAs. Additionally, some automata constructions preserve the structural properties of given regular expressions; for example, the Thompson construction [17] or the position construction =-=[8, 14]-=-. Recently, Giammarresi et al. [7] introduced Thompson languages and simple Thompson languages based on the structural properties of Thompson automata. One interesting property of simple Thompson lang... |

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Citation Context ...ce A ′ can accept a string with length m − 1, Lp of a state whose level is i accepts a string with length m − 1 − i. We say that a DFA A ′ is minimal if and only if Lp �= Lq for any two states in A ′ =-=[18]-=-. If Lp = Lq, then we say p and q are equivalent; for example, two states p and q at the third level in Fig. 8 are equivalent and, therefore, A ′ is not minimal. Lemma 4. If two states p and q are at ... |

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Citation Context ...pressions from FAs. Additionally, some automata constructions preserve the structural properties of given regular expressions; for example, the Thompson construction [17] or the position construction =-=[8, 14]-=-. Recently, Giammarresi et al. [7] introduced Thompson languages and simple Thompson languages based on the structural properties of Thompson automata. One interesting property of simple Thompson lang... |

69 | Two-dimensional languages
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Citation Context ... automata constructions preserve the structural properties of given regular expressions; for example, the Thompson construction [17] or the position construction [8, 14]. Recently, Giammarresi et al. =-=[7]-=- introduced Thompson languages and simple Thompson languages based on the structural properties of Thompson automata. One interesting property of simple Thompson languages is that for a given Thompson... |

29 |
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Citation Context ...A into a (traditional) FA by the sequence of state expansions. We expand each regular expression in a transition of A until the expression is either a single character or the null-string. Ilie and Yu =-=[11]-=- adopted this idea of state expansion and proposed an NFA construction with λ, which is a compact Thompson construction 2 . 2 Ilie and Yu [11] called the construction the ǫNFA construction, where ǫ de... |

23 | Characterization of Glushkov automata - Caron, Ziadi - 2000 |

16 | The generalization of generalized automata: expression automata
- Han, Wood
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(Show Context)
Citation Context ...l properties to satisfy a certain condition. For example, a deterministic finite-state automaton (DFA) should not have any out-transitions from a final state if the DFA defines a prefix-free language =-=[9]-=-. Given a nondeterministic finite-state automaton (NFA) A, if L(A) is outfix-free, then there are no cycles in A since ∗ Han and Wood were supported under the Research Grants Council of Hong Kong Comp... |

15 |
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(Show Context)
Citation Context ... no Kleene stars in transitions. Furthermore, we can transform an EA into a traditional FA using state expansion. 3.5 State expansion State elimination was introduced by Brzozowski and McCluskey, Jr. =-=[3]-=- to compute regular expressions from FAs. State elimination maintains the language accepted by a given automaton while removing states; EAs can be used as a data structure for state elimination. State... |

8 | Deterministic generalized automata
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(Show Context)
Citation Context ...; they allow regular languages on transitions instead of single characters. If we only allow characters on transitions, then A is an FA and if we only allow strings, then A is a generalized automaton =-=[4, 5]-=-. Since the strongly connected components of a directed graph can be computed in linear time [1], we can identify all orbits of A in linear time in |A|. Once we identify orbits, then we compute all si... |

7 |
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(Show Context)
Citation Context ...so compute the simple-regular language of a position automaton since both the Thompson automata [17] and the position automata [8, 14] essentially have the same structure for same regular expressions =-=[6]-=-. 4 Conclusions We have introduced simple-regular expressions and languages. Given an outfix-free regular language L and an FA A for L, all strings in L must be spelled out by simple paths. On the oth... |

7 |
Enumerating all simple paths in a graph
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(Show Context)
Citation Context ...lar expressions and languages and design algorithms for computing simple-regular expressions and languages. The algorithm for computing simple-regular language of a given FA is based on the algorithm =-=[16]-=- for enumerating all simple paths. Then, we investigate the complexity blowup from an FA A to its simple-regular language FA A ′ . We also consider when A is a Thompson automaton or a position automat... |

5 | A characterization of thompson digraphs - Giammarresi, Ponty, et al. - 2004 |

5 | Outfix-free Regular Languages and Prime Outfix-free decomposition”, Fundamenta Informaticae XX - Han, Wood - 2007 |

4 | Deterministic generalized automata, Theoretical Computer Science 215 - Giammarresi, Montalbano - 1999 |

3 | McCluskey Jr., Signal flow graph techniques for sequential circuit state diagrams - Brzozowski, E - 1963 |

1 |
Outfix-free regular expressions and languages. manuscript submitted for publication
- Han, Wood
- 2005
(Show Context)
Citation Context ...of an outfix-free regular language in an FA must be simple. Furthermore, since an outfixfree regular language L is finite, there is an acyclic deterministic finite-state automaton for L. Han and Wood =-=[10]-=- designed an algorithm for determining the outfix-freeness of a given acyclic deterministic finite-state automaton based on the structural properties of outfix-free languages. FAs are directed graphs ... |