Reports de recerca
http://hdl.handle.net/2117/3488
2020-11-26T04:44:00ZAdaptive logspace reducibility and parallel time
http://hdl.handle.net/2117/330912
Adaptive logspace reducibility and parallel time
Álvarez Faura, M. del Carme; Balcázar Navarro, José Luis; Jenner, Birgit
We discuss two notions of functional oracle for logarithmic space-bounded machines, which differ in whether there is only one oracle tape for both the query and the answer or a separate tape for the answer, which can still be read on while the next query is already being constructed. The first notion turns out to be basically non-adaptive, behaving like access to an oracle set. The second notion, on the other hand, is adaptive. By imposing appropriate bounds on the number of functional oracle queries made in this computation model, we obtain new characterizations of the NC and AC hierarchies; thus the number of oracle queries can be considered as a measure of parallel time. Using this characterization of parallel classes, we solve open questions of Wilson.
2020-10-28T11:22:14ZÁlvarez Faura, M. del CarmeBalcázar Navarro, José LuisJenner, BirgitWe discuss two notions of functional oracle for logarithmic space-bounded machines, which differ in whether there is only one oracle tape for both the query and the answer or a separate tape for the answer, which can still be read on while the next query is already being constructed. The first notion turns out to be basically non-adaptive, behaving like access to an oracle set. The second notion, on the other hand, is adaptive. By imposing appropriate bounds on the number of functional oracle queries made in this computation model, we obtain new characterizations of the NC and AC hierarchies; thus the number of oracle queries can be considered as a measure of parallel time. Using this characterization of parallel classes, we solve open questions of Wilson.An approach to correctness of data parallel algorithms
http://hdl.handle.net/2117/328707
An approach to correctness of data parallel algorithms
Gabarró Vallès, Joaquim; Gavaldà Mestre, Ricard
The design of data parallel algorithms for fine-grained SIMD machines is a fundamental domain in today computer science. High standards in the specification and resolution of problems have been achieved in the sequential case. It seems reasonable to apply the same level of quality to data parallel programs. It appears that most of the data parallel problems can be specified in terms of post and preconditions. These conditions characterize the overall state of the fine-grained processors in the initial and final states. In this paper: We present an axiomatic system to prove correctness of data parallel algorithms on fine-grained SIMD machines. We specify some data parallel problems like tree sum, radix sorting, and dynamic memory allocation. With this set of axioms we prove the correctness of programs solving the above problems. It seems that the framework to deal with data parallel problems is quite different from the other one dealing with problems of parallelism with multiple threads of control, like those solvable in CSP.
2020-09-14T09:45:42ZGabarró Vallès, JoaquimGavaldà Mestre, RicardThe design of data parallel algorithms for fine-grained SIMD machines is a fundamental domain in today computer science. High standards in the specification and resolution of problems have been achieved in the sequential case. It seems reasonable to apply the same level of quality to data parallel programs. It appears that most of the data parallel problems can be specified in terms of post and preconditions. These conditions characterize the overall state of the fine-grained processors in the initial and final states. In this paper: We present an axiomatic system to prove correctness of data parallel algorithms on fine-grained SIMD machines. We specify some data parallel problems like tree sum, radix sorting, and dynamic memory allocation. With this set of axioms we prove the correctness of programs solving the above problems. It seems that the framework to deal with data parallel problems is quite different from the other one dealing with problems of parallelism with multiple threads of control, like those solvable in CSP.A positive relativization of polynomial time vs. polylog space
http://hdl.handle.net/2117/328495
A positive relativization of polynomial time vs. polylog space
Gavaldà Mestre, Ricard
Can every set in P be solved in polylogarithmic space? We show that this question is equivalent to asking whether the classes PSPACE and EXPTIME are always equal under relativization. We use an oracle access mechanism that is fair, in the sense that it maintains all known relationships between unrelativized PSPACE and EXPTIME.
2020-09-07T17:37:18ZGavaldà Mestre, RicardCan every set in P be solved in polylogarithmic space? We show that this question is equivalent to asking whether the classes PSPACE and EXPTIME are always equal under relativization. We use an oracle access mechanism that is fair, in the sense that it maintains all known relationships between unrelativized PSPACE and EXPTIME.Adaptive logspace and depth-bounded reducibilities
http://hdl.handle.net/2117/328494
Adaptive logspace and depth-bounded reducibilities
Balcázar Navarro, José Luis
We discuss a number of results regarding an important subject: the study of the computational power of depth-bounded reducibilities, their use to classify the complexity of computational problems, and their characterizations in terms of other computational models. In particular, problems arising in the design of concurrent systems are studied, and two kinds of logarithmic space reductions are defined. The first one is nonadaptive and equivalent in many respects to the oracle set model. The second one provides a notion of adaptive logspace reducibility which turns out to characterize precisely depth-bounded reductions. The closures of NP under these reducibilities are also treated. This is a conference delivered at Structure in Complexity Theory 6th Annual Conference, Chicago 1991, and appears in the proceedings in the present form.
2020-09-07T16:51:00ZBalcázar Navarro, José LuisWe discuss a number of results regarding an important subject: the study of the computational power of depth-bounded reducibilities, their use to classify the complexity of computational problems, and their characterizations in terms of other computational models. In particular, problems arising in the design of concurrent systems are studied, and two kinds of logarithmic space reductions are defined. The first one is nonadaptive and equivalent in many respects to the oracle set model. The second one provides a notion of adaptive logspace reducibility which turns out to characterize precisely depth-bounded reductions. The closures of NP under these reducibilities are also treated. This is a conference delivered at Structure in Complexity Theory 6th Annual Conference, Chicago 1991, and appears in the proceedings in the present form.Characterizations of some complexity classes between [theta sub 2 super p] and [delta sub 2 super p]
http://hdl.handle.net/2117/328115
Characterizations of some complexity classes between [theta sub 2 super p] and [delta sub 2 super p]
Castro Rabal, Jorge; Seara Ojea, Carlos
We give some characterizations of the classes P super NP [0(log super k n)]. First, we show that these classes are equal to classes AC super k-1 (N P). Second, we prove that they are also equivalent to some classes defined in the Extended Boolean hierarchy. Finally, we show that there exists a strong connection between classes defined by polynomial time Turing machines with few queries to an N P oracle and classes defined by small size circuits with N P oracle gates. With these results we solve open questions arosed by K. W. Wagner and by E. Allender and C.B. Wilson.
2020-07-30T17:42:15ZCastro Rabal, JorgeSeara Ojea, CarlosWe give some characterizations of the classes P super NP [0(log super k n)]. First, we show that these classes are equal to classes AC super k-1 (N P). Second, we prove that they are also equivalent to some classes defined in the Extended Boolean hierarchy. Finally, we show that there exists a strong connection between classes defined by polynomial time Turing machines with few queries to an N P oracle and classes defined by small size circuits with N P oracle gates. With these results we solve open questions arosed by K. W. Wagner and by E. Allender and C.B. Wilson.Generalized Kolmogorov complexity in relativized separations
http://hdl.handle.net/2117/328102
Generalized Kolmogorov complexity in relativized separations
Gavaldà Mestre, Ricard; Torenvliet, Leen; Watanabe, Osamu; Balcázar Navarro, José Luis
We describe several developments of a technique, due to Hartmanis, that uses Kolmogorov complexity to prove the existence of relativizations separating complexity classes. The main advantage of these proofs is that they clearly show the limitations of certain classes of oracle machines and the relevance of these limitations for the proof. Such limitations refer to the extent to which the machines defining the class are able to process Kolmogorov-complex structures.
2020-07-30T16:24:57ZGavaldà Mestre, RicardTorenvliet, LeenWatanabe, OsamuBalcázar Navarro, José LuisWe describe several developments of a technique, due to Hartmanis, that uses Kolmogorov complexity to prove the existence of relativizations separating complexity classes. The main advantage of these proofs is that they clearly show the limitations of certain classes of oracle machines and the relevance of these limitations for the proof. Such limitations refer to the extent to which the machines defining the class are able to process Kolmogorov-complex structures.Functional oracle queries as a measure of parallel time
http://hdl.handle.net/2117/327984
Functional oracle queries as a measure of parallel time
Álvarez Faura, M. del Carme; Balcázar Navarro, José Luis; Jenner Núñez, Birgit
We discuss two notions of functional oracle for logarithmic space-bounded machines, which differ in whether there is only one oracle tape for both the query and the answer or a separate tape for the answer, which can still be read on while the following query is already being constructed.
The first notion turns out to be basically non-adaptive, behaving like access to an oracle set. The second notion, on the other hand, is adaptive. By imposing appropriate bounds on the number of functional oracle queries made in this computation model, we obtain new characterizations of the NC and AC hierarchies; thus the number of oracle queries can be considered as a measure of parallel time. Using this characterization of parallel classes, we solve open questions of Wilson.
2020-07-29T13:17:28ZÁlvarez Faura, M. del CarmeBalcázar Navarro, José LuisJenner Núñez, BirgitWe discuss two notions of functional oracle for logarithmic space-bounded machines, which differ in whether there is only one oracle tape for both the query and the answer or a separate tape for the answer, which can still be read on while the following query is already being constructed.
The first notion turns out to be basically non-adaptive, behaving like access to an oracle set. The second notion, on the other hand, is adaptive. By imposing appropriate bounds on the number of functional oracle queries made in this computation model, we obtain new characterizations of the NC and AC hierarchies; thus the number of oracle queries can be considered as a measure of parallel time. Using this characterization of parallel classes, we solve open questions of Wilson.Deciding bisimilarity is P-complete
http://hdl.handle.net/2117/327610
Deciding bisimilarity is P-complete
Balcázar Navarro, José Luis; Gabarró Vallès, Joaquim; Santha, Miklos
On finite labelled transition systems, the problems of deciding strong bisimilarity, observation equivalence, and observation congruence are P-complete under many-one NC-reducibility. As a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of an efficient parallel algorithm to solve any of these problems will require an exceedingly hard algorithmic breakthrough.
2020-07-24T14:19:56ZBalcázar Navarro, José LuisGabarró Vallès, JoaquimSantha, MiklosOn finite labelled transition systems, the problems of deciding strong bisimilarity, observation equivalence, and observation congruence are P-complete under many-one NC-reducibility. As a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of an efficient parallel algorithm to solve any of these problems will require an exceedingly hard algorithmic breakthrough.Parallel complexity in the design and analysis of concurrent systems
http://hdl.handle.net/2117/191920
Parallel complexity in the design and analysis of concurrent systems
Álvarez Faura, M. del Carme; Balcázar Navarro, José Luis; Gabarró Vallès, Joaquim
We study the parallel complexity of three problems on concurrency: decision of firing sequences for Petri nets, trace equivalence for partially commutative monoids, and strong bisimilarity in finite transition systems. We show that the first two problems can be efficiently parallelized, allowing logarithmic time Parallel RAM algorithms and even constant time unbounded fan-in circuits with threshold gates. However, lower bounds imply that they cannot be solved in constant time by a PRAM algorithm. On the other hand, strong bisimilarity in finite labelled transition systems can be classified as P-complete; as a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of an efficient parallel algorithm to solve any of these problems will require an exceedingly hard algorithmic breakthrough.
2020-06-29T15:47:58ZÁlvarez Faura, M. del CarmeBalcázar Navarro, José LuisGabarró Vallès, JoaquimWe study the parallel complexity of three problems on concurrency: decision of firing sequences for Petri nets, trace equivalence for partially commutative monoids, and strong bisimilarity in finite transition systems. We show that the first two problems can be efficiently parallelized, allowing logarithmic time Parallel RAM algorithms and even constant time unbounded fan-in circuits with threshold gates. However, lower bounds imply that they cannot be solved in constant time by a PRAM algorithm. On the other hand, strong bisimilarity in finite labelled transition systems can be classified as P-complete; as a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of an efficient parallel algorithm to solve any of these problems will require an exceedingly hard algorithmic breakthrough.Computational complexity of small descriptions
http://hdl.handle.net/2117/191725
Computational complexity of small descriptions
Gavaldà Mestre, Ricard; Watanabe, Osamu
For a set L that is polynomial time reducible (in short, = sub T super P-reducible) to some sparse set, we investigate the computational complexity of such sparse sets relative to L. We construct sets A and B such that both of them are = sub T super P-reducible to some sparse set, but A (resp., B) is = sub T super P-reducible to no sparse set in P super A (resp., NP super B ¿ co-NP super B); that is, the complexity of sparse sets to which A (resp., B) is = sub T super P-reducible is more than P super A (resp., NP super B ¿ co-NP super B). Some consequences of these results and applications of our proof technique are also discussed.
2020-06-26T14:44:57ZGavaldà Mestre, RicardWatanabe, OsamuFor a set L that is polynomial time reducible (in short, = sub T super P-reducible) to some sparse set, we investigate the computational complexity of such sparse sets relative to L. We construct sets A and B such that both of them are = sub T super P-reducible to some sparse set, but A (resp., B) is = sub T super P-reducible to no sparse set in P super A (resp., NP super B ¿ co-NP super B); that is, the complexity of sparse sets to which A (resp., B) is = sub T super P-reducible is more than P super A (resp., NP super B ¿ co-NP super B). Some consequences of these results and applications of our proof technique are also discussed.