# Equations in free semigroups with involution and their relation to equations in free groups

@inproceedings{Gutirrez2000EquationsIF, title={Equations in free semigroups with involution and their relation to equations in free groups}, author={Claudio Guti{\'e}rrez}, booktitle={Theor. Comput. Sci.}, year={2000} }

## 3 Citations

### Satisfiability of equations in free groups is in PSPACE

- MathematicsSTOC '00
- 2000

We prove that the computational complexity of the problem of deciding if an equation in a free group has a solution is PSPACE. The problem was proved decidable in 1982 by Makanin, w h o s e algorithm…

### The existential theory of equations with rational constraints in free groups is PSPACE-complete

- MathematicsInf. Comput.
- 2001

## References

SHOWING 1-10 OF 19 REFERENCES

### Satisfiability of word equations with constants is in exponential space

- MathematicsProceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
- 1998

This paper proves the stronger fact that Makanin's algorithm (1977), a general procedure to decide if a word equation has a solution, is single exponential, while reducing it to triple exponential, and conjecturing that it could be brought down to double exponential.

### Satisfiability of equations in free groups is in PSPACE

- MathematicsSTOC '00
- 2000

We prove that the computational complexity of the problem of deciding if an equation in a free group has a solution is PSPACE. The problem was proved decidable in 1982 by Makanin, w h o s e algorithm…

### Satisfiability of word equations with constants is in PSPACE

- Mathematics40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
- 1999

It is proved that satisfiability problem for word equations is in PSPACE, and the solution to this problem can be deduced from the inequality of the EPTs.

### The existential theory of equations with rational constraints in free groups is PSPACE-complete

- MathematicsInf. Comput.
- 2001

### Makanin's algorithm for solving word equations with regular constraints

- Mathematics
- 1998

We give a self-contained proof of a fundamental result of Makanin (1977), which solves the satisfiability problem of equations with constants over free monoids. Our presentation of Makanin's…

### Combinatorics on words

- Mathematics
- 1997

1. Words D. Perrin 2. Square free words and idempotent semigroups J. Berstel and C. Reutenauer 3. Van der Waerden's theorem J. E. Pin 4. Repetitive mappings and morphisms G. Pirillo 5. Factorizations…

### ON SYSTEMS OF EQUATIONS IN A FREE GROUP

- Mathematics
- 1985

A description of the general solution of given bounded periodicity exponent is obtained for an arbitrary system of equations in a free group. On the basis of this result an algorithm is constructed…

### Complexity of Makanin's algorithm

- Computer ScienceJACM
- 1996

It is proved that the exponent of periodicity of a minimal solution of a word equation is of order 2, which implies an exponential improvement of known upper bounds on complexity of word-unification algorithms.

### Satisfiability of word equations with constants is in NEXPTIME

- Mathematics, Computer ScienceSTOC '99
- 1999

It is proved that the length of a shortest solution of a word equation of length n can bounded by a double exponential function in n and proves that the problem of solvability of word equations is in NEXPTIME.