It is available at github.
A manual of how to use it is available on the
arxiv.
There is also a text file with some
examples of
how to use `Walnut`.

If you find Walnut useful in your research, please be sure to cite Hamoon Mousavi as the author of the software, and let me know what you achieved with it.

Walnut has been used in a variety of papers. A partial list is here (will be updated):

- James Currie, Narad Rampersad, Tero Harju, and Pascal Ochem, Some further results on squarefree arithmetic progressions in infinite words, arxiv preprint, January 18 2019.
- James Currie and Narad Rampersad, On some problems of Harju concerning squarefree arithmetic progressions in infinite words, arxiv preprint, December 5 2018.
- Lukasz Merta, Formal inverses of the generalized Thue-Morse sequences and variations of the Rudin-Shapiro sequence, arxiv preprint, October 8 2018.
- Colin Krawchuk and Narad Rampersad,
Cyclic Complexity of Some Infinite Words and Generalizations,
*Integers***18A**(2018), #A12. - Jeffrey Shallit and Ramin Zarifi, Circular critical exponents for Thueâ€“Morse factors, RAIRO Info. Theor., published online 17 January 2019. Available here.
- Pierre Bonardo, Anna E. Frid, Jeffrey Shallit,
"The number of valid factorizations of Fibonacci prefixes",
*Theor. Comput. Sci.*, 2019, to appear. Available online at https://doi.org/10.1016/j.tcs.2018.12.016. -
Jason Bell, Kathryn Hare and Jeffrey Shallit,
When is an automatic set an additive basis?
*Proc. Amer. Math. Soc. Ser. B***5**(2018), 50-63. Available here. - Jason Bell, Thomas Finn Lidbetter, and Jeffrey Shallit,
Additive Number Theory via Approximation by Regular Languages,
arxiv preprint, April 23 2018. Appeared in M. Hoshi and S. Seki, eds.,
DLT 2018, LNCS Vol. 11088, Springer, 2018, pp. 121-132.
Here are text files describing how you can verify the results
yourself using
`Grail`and`Walnut`. - Narad Rampersad, Jeffrey Shallit, Élise Vandomme,
Critical exponents of infinite balanced words, arxiv preprint,
January 16 2018. Accepted for
*Theoretical Computer Science*; in press here. - James Currie, Lucas Mol, and Narad Rampersad,
A family of formulas with reversal of high avoidability index,
*International Journal of Algebra and Computation***27**(2017) 477-493. - Chen Fei Du, Hamoon Mousavi, Eric Rowland, Luke Schaeffer, and Jeffrey Shallit, Decision Algorithms for Fibonacci-Automatic Words, II: Related Sequences and Avoidability,
*Theoret. Comput. Sci.***657**(2017), 146-162. Examples from the paper that can be run with`Walnut`(download`Walnut`below):- Thue-Morse examples
- Rudin-Shapiro examples
- Rudin-Shapiro example for trapezoidal words
- paperfolding sequence examples
- paperfolding example for trapezoidal words
- period-doubling examples
- Fibonacci examples

- RS.txt (automaton for Rudin-Shapiro)
- P.txt (msd automaton for paperfolding)
- PR.txt (lsd automaton for paperfolding)
- PD.txt (automaton for period-doubling)

- Quentin Valembois, Propriétés décidables des suites automatiques, Master's thesis, University of Liège, Belgium, 2017. Available here.
- Luke Schaeffer and Jeffrey Shallit,
Closed, Palindromic, Rich, Privileged, Trapezoidal, and Balanced Words in Automatic Sequences,
*Elect. J. Combinatorics***23**(1) (2016), Paper #P1.25. - Chen Fei Du, Hamoon Mousavi, Luke Schaeffer, and Jeffrey Shallit,
Decision Algorithms for Fibonacci-Automatic
Words, III: Enumeration and Abelian Properties,
*Int. J. Found. Comput. Sci.***27**(8) (2016), 943-963. - Hamoon Mousavi, Luke Schaeffer, and Jeffrey Shallit,
Decision Algorithms for Fibonacci-Automatic Words, I: Basic Results,
*RAIRO Inform. Théorique***50**(2016), 39-66. E-version: here - H. Mousavi and J. Shallit,
Mechanical Proofs of Properties of the Tribonacci Word,
in
F. Manea and D. Nowotka, eds.,
WORDS 2015, LNCS 9304, Springer, 2015, pp. 1-21. Here are the
Walnut predicates you can use to reproduce most of the results in this
paper:
- predicates
- TR.txt, put in the "Word Automata" library

- Daniel Goc, Narad Rampersad, Michel Rigo, Pavel Salimov,
On the number of Abelian Bordered Words (with an Example of Automatic Theorem-Proving)
*Int. J. Found. Comput. Sci.***25**(2014), 1097-1110.