# 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…

## 17 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.

### On the Mother of All Automata: The Position Automaton

- Computer ScienceDLT
- 2017

New relations to the taxonomy of different conversions from regular expressions to equivalent finite automata are contributed and it turns out that although the conversion of regular expressions and reversal of regular Expression to finite Automata seems quite similar, there are significant differences.

### Solving of Regular Equations Revisited (extended version)

- Mathematics, Computer ScienceArXiv
- 2019

It is shown that operations such as subtraction and shuffling can be expressed via some appropriate set of regular equations and obtained direct (algebraic) methods without having to convert to and from finite automaton.

### State complexity of permutation on finite languages over a binary alphabet

- Computer Science, MathematicsTheor. Comput. Sci.
- 2017

### A deterministic parsing algorithm for ambiguous regular expressions

- Computer ScienceActa Informatica
- 2020

A new parser generator, called Berry–Sethi Parser (BSP), is introduced, for ambiguous regular expressions (RE), which constructs a deterministic finite-state transducer that recognizes an input string and additionally outputs a linear representation of all the syntax trees of the string.

### 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, which enables the standard characterization of ldl 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.

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