# From Finite Automata to Regular Expressions and Back-A Summary on Descriptional Complexity

@inproceedings{Gruber2014FromFA, title={From Finite Automata to Regular Expressions and Back-A Summary on Descriptional Complexity}, author={Hermann Gruber and Markus Holzer}, booktitle={AFL}, year={2014} }

The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free nondeterministic devices. Moreover…

## 16 Citations

Conversion of Deterministic and Non-Deterministic Finite Automata to Regular Expression using Brzozowski Algebraic Method

- Computer Science
- 2020

For conversion of deterministic and nondeterministic finite automata to regular expression, Brzozowski Algebraic method, also known as Arden's Theorem is used in this paper because of its simplicity and straight forwardness.

Constrained Expressions and their Derivatives

- MathematicsFundam. Informaticae
- 2016

This paper proposes an extension to classical regular expressions by the addition of two operators allowing the inclusion of boolean formulae from the zeroth order logic called constrained expressions, and shows that the language associated when both interpretation and realization are fixed is stricly regular and can be not regular otherwise.

The Formal Language Theory Column

- Computer Science
- 2015

This work states that by suitably restricting more general models such as context-free grammars, pushdown automata, and Turing machines, that characterize wider classes of languages, it is possible to obtain formal models that generate or recognize regular languages only.

Regular Expression Length via Arithmetic Formula Complexity

- Computer Science, MathematicsDCFS
- 2020

Lower bounds on the length of regular expressions for finite languages by methods from arithmetic circuit complexity and a lower bound method for multilinear arithmetic formulas by so-called log-product polynomials to regular expressions are proved.

Monitoring Constraints and Metaconstraints with Temporal Logics on Finite Traces

- Computer ScienceArXiv
- 2020

It is shown that LDLf is able to declaratively express, in the logic itself, not only the constraints to be monitored, but also the de-facto standard RV-LTL monitors, and this enables us to directly employ the standard characterization of LDLf based on finite-state automata to monitor constraints in a fine-grained way.

Learning Interpretable Models in the Property Specification Language

- Computer ScienceIJCAI
- 2020

This work develops a learning algorithm for formulas in the IEEE standard temporal logic PSL (Property Specification Language), motivated by the fact that many natural properties cannot be expressed in LTL, whereas it is easy to express such properties in PSL.

Structured Algorithm for Software Behavior Model based on Finite State Automaton

- Computer Science
- 2018

This paper analyzes the topology structure algorithm of software behavior model and proposes FSM Diff algorithm based on finite state automaton, which is more effective to select the key state nodes in the software running state diagram.

Subsequences With Gap Constraints: Complexity Bounds for Matching and Analysis Problems

- Mathematics, Computer ScienceArXiv
- 2022

It is proved that tight (conditional on the orthogonal vectors (OV) hypothesis) complexity bounds for checking whether a given p is a gc -subsequence of a string w are proved.

Regularity of k-Abelian Equivalence Classes of Fixed Cardinality

- MathematicsAdventures Between Lower Bounds and Higher Altitudes
- 2018

It is shown that, for any fixed integer \(r\ge 1\), the language of words representing equivalence classes of cardinality r is regular.

Binary Expression of Ancestors in the Collatz Graph

- Mathematics, Computer ScienceRP
- 2020

This paper implements the algorithm which generates the regular expression, $\texttt{reg}_k(x)$ for any $x$ and $k, and gives a new exploratory tool for further study of the Collatz graph in binary.

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