# Automata in SageMath - Combinatorics meet Theoretical Computer Science

@article{Heuberger2014AutomataIS, title={Automata in SageMath - Combinatorics meet Theoretical Computer Science}, author={Clemens Heuberger and Daniel Krenn and Sara Kropf}, journal={Discret. Math. Theor. Comput. Sci.}, year={2014}, volume={18} }

The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. Several combinatorial problems, in particular digit problems, are introduced, modeled by automata and transducers and solved using SageMath. In particular, we compute the asymptotic Hamming weight of a non-adjacent-form-like digit expansion, which was not known before.

## 5 Citations

### Application of Smirnov Words to Waiting Time Distributions of Runs

- MathematicsElectron. J. Comb.
- 2017

Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the…

### Variances and covariances in the Central Limit Theorem for the output of a transducer

- Mathematics, Computer ScienceEur. J. Comb.
- 2015

### Analysis of carries in signed digit expansions

- MathematicsMonatshefte fur Mathematik
- 2017

The number of positive and negative carries in the addition of two independent random signed digit expansions of given length is analyzed asymptotically for the (q, d)-system and the symmetric signed digit expansion and the results include expectation, variance, covariance and convergence to a central limit theorem.

### Output Sum of Transducers: Limiting Distribution and Periodic Fluctuation

- Mathematics, Computer ScienceElectron. J. Comb.
- 2015

The abelian complexity function of the paperfolding sequence is analyzed and it turns out that the sequence is asymptotically normally distributed for many transducers.

### Haydi: Rapid Prototyping and Combinatorial Objects

- Computer ScienceFoIKS
- 2018

The goal of this paper is to give the overall picture of Haydi together with a formal definition for the case of generating canonical forms.

## References

SHOWING 1-10 OF 44 REFERENCES

### On the performance of automata minimization algorithms

- Computer Science
- 2007

This paper compares the running time of four minimization algorithms based on experimental results and applies these algorithms to both deterministic and nondeterministic random automata.

### Elements of Automata Theory

- Computer Science
- 2009

This treatise gives a rigorous account of the topic and illuminates its real meaning by looking at the subject in a variety of ways, including notions of rationality and recognisability.

### Introduction to automata theory, languages, and computation, 2nd edition

- Computer ScienceSIGA
- 2001

The introduction to formal languages and automata wasolutionary rather than rcvolrrtionary and addressed Initially, I felt that giving solutions to exercises was undesirable hecause it lirrritcd the Chapter 1 fntroduction to the Theory of Computation.

### Scalar Multiplication on Koblitz Curves Using the Frobenius Endomorphism and Its Combination with Point Halving: Extensions and Mathematical Analysis

- Mathematics, Computer ScienceAlgorithmica
- 2006

The optimality and other properties of the τ-adic nonadjacent form is proved: this expansion has been introduced in order to compute scalar multiplications on Koblitz curves efficiently and is proved to be optimal.

### Minimal expansions in redundant number systems: Fibonacci bases and Greedy algorithms

- MathematicsPeriod. Math. Hung.
- 2004

A unique minimal expansion is described and a greedy algorithm to compute it is given for the Fibonacci case and transducers to calculate minimal expansions from other expansions are given.

### Positional number systems with digits forming an arithmetic progression

- Mathematics, Computer Science
- 2008

A novel digit system that arises in a natural way in a graph-theoretical problem and is defined by a set of positive digits forming an arithmetic progression and a complete residue system modulo the base b is studied.

### Introduction to Coding Theory

- Computer Science
- 1982

This third edition has been revised and expanded, including new chapters on algebraic geometry, new classes of codes, and the essentials of the most recent developments on binary codes.

### Analysis of Alternative Digit Sets for Nonadjacent Representations

- Mathematics
- 2006

Abstract.It is known that every positive integer n can be represented as a finite sum of the form ∑iai2i, where ai ∈ {0, 1,−1} and no two consecutive ai’s are non-zero (“nonadjacent form”, NAF).…

### Variances and covariances in the Central Limit Theorem for the output of a transducer

- Mathematics, Computer ScienceEur. J. Comb.
- 2015