Claudio Gutierrez - Academia.edu (original) (raw)
Papers by Claudio Gutierrez
Information and Computation/information and Control, 2005
It is known that the existential theory of equations in free groups is decidable. This is a famou... more It is known that the existential theory of equations in free groups is decidable. This is a famous result of Makanin. On the other hand it has been shown that the scheme of his algorithm is not primitive recursive. In this paper we present an algorithm that works in polynomial space, even in the more general setting where each variable has a rational constraint, that is, the solution has to respect a specification given by a regular word language. Our main result states that the existential theory of equations in free groups with rational constraints is PSPACE-complete. We obtain this result as a corollary of the corresponding statement about free monoids with involution.
Computing Research Repository, 2001
This paper extends extends known results on the complexity of word equations and equations in fre... more This paper extends extends known results on the complexity of word equations and equations in free groups in order to include the presence of rational constraints, i.e., such that a possible solution has to respect a specification given by a rational language. Our main result states that the existential theory of equations with rational constraints in free groups is PSPACE-complete.
This superscalar microprocessor is the first 64 b implementation of the PowerPC architecture. Wit... more This superscalar microprocessor is the first 64 b implementation of the PowerPC architecture. With estimated performance levels of 225 SPECint92 and 300 SPECfp92 at a nominal processor frequency of 133 MHz and a 4ML2 operating at 67 MHz, this processor delivers balanced performance suitable for high-end workstations and servers. The chip is realized in n-well 0.5 /spl mu/m CMOS with p-epi on a p/sup +/ substrate. There are four layers of metallization. The processor contains 6.88M transistors and dissipates an estimated 30 W at 133 MHz from a 3.3 V power supply. The 18.2/spl times/17.1 mm/sup 2/ die is packaged in a 25/spl times/25 ball grid array.
In this paper we study solvability of equations over free semigroups, known as word equations, pa... more In this paper we study solvability of equations over free semigroups, known as word equations, particularly G.S. Makanin's algorithm (1977), a general procedure to decide if a word equation has a solution. The upper bound time-complexity of Makanin's original decision procedure was quadruple exponential in the length of the equation, as shown by Jaffar. A. Koscielski and L. Pacholski (1996) reduced it to triple exponential, and conjectured that it could be brought down to double exponential. The present paper proves this conjecture. In fact we prove the stronger fact that its space-complexity is single exponential
We prove that the computational complexity of the problem of deciding if an equation in a free gr... more 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, whose algorithm was proved later to be non primitive recursive: this was the best upper bound known for this problem. Our proof consists in reducing equations in free groups to equations in free semigroups with antiinvolution, and presenting an algorithm for deciding equations in free semigroups with antiinvolution.
Information and Computation/information and Control, 2005
It is known that the existential theory of equations in free groups is decidable. This is a famou... more It is known that the existential theory of equations in free groups is decidable. This is a famous result of Makanin. On the other hand it has been shown that the scheme of his algorithm is not primitive recursive. In this paper we present an algorithm that works in polynomial space, even in the more general setting where each variable has a rational constraint, that is, the solution has to respect a specification given by a regular word language. Our main result states that the existential theory of equations in free groups with rational constraints is PSPACE-complete. We obtain this result as a corollary of the corresponding statement about free monoids with involution.
Computing Research Repository, 2001
This paper extends extends known results on the complexity of word equations and equations in fre... more This paper extends extends known results on the complexity of word equations and equations in free groups in order to include the presence of rational constraints, i.e., such that a possible solution has to respect a specification given by a rational language. Our main result states that the existential theory of equations with rational constraints in free groups is PSPACE-complete.
This superscalar microprocessor is the first 64 b implementation of the PowerPC architecture. Wit... more This superscalar microprocessor is the first 64 b implementation of the PowerPC architecture. With estimated performance levels of 225 SPECint92 and 300 SPECfp92 at a nominal processor frequency of 133 MHz and a 4ML2 operating at 67 MHz, this processor delivers balanced performance suitable for high-end workstations and servers. The chip is realized in n-well 0.5 /spl mu/m CMOS with p-epi on a p/sup +/ substrate. There are four layers of metallization. The processor contains 6.88M transistors and dissipates an estimated 30 W at 133 MHz from a 3.3 V power supply. The 18.2/spl times/17.1 mm/sup 2/ die is packaged in a 25/spl times/25 ball grid array.
In this paper we study solvability of equations over free semigroups, known as word equations, pa... more In this paper we study solvability of equations over free semigroups, known as word equations, particularly G.S. Makanin's algorithm (1977), a general procedure to decide if a word equation has a solution. The upper bound time-complexity of Makanin's original decision procedure was quadruple exponential in the length of the equation, as shown by Jaffar. A. Koscielski and L. Pacholski (1996) reduced it to triple exponential, and conjectured that it could be brought down to double exponential. The present paper proves this conjecture. In fact we prove the stronger fact that its space-complexity is single exponential
We prove that the computational complexity of the problem of deciding if an equation in a free gr... more 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, whose algorithm was proved later to be non primitive recursive: this was the best upper bound known for this problem. Our proof consists in reducing equations in free groups to equations in free semigroups with antiinvolution, and presenting an algorithm for deciding equations in free semigroups with antiinvolution.