C. ` Alvarez, J. D'iaz, and J. Tor'an. Complexity classes with complete problems between P and NP-C. In Proc. of Conf. on Funfamentals of Computation Theory, number 380 in LNCS, pages 13--25. Springer, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be nondeterministic, and use at most h(n) space. A well known example of such a class is the fi k hierarchy of NP machines making at most O(log k n) nondeterministic steps, i.e. fi k = TINOSP(pol; log k ; pol) which lies between P and NP and has complete problems for each of its level (see [1]) Other examples of bounded nondeterminism can be found in [3, 7, 12] We start by stating some simple properties of bounded nondeterminism classes: TINOSP( f(n) NSPACE(f(n) TINOSP( 0; f(n) TINOSP( f(n) f (n) DSPACE(f(n) TINOSP(pol; f(n) NTISP(pol; ....

....we use the noneraser version of an index tape, which is not necessarily erased after each use. 5 Observe that NTIME(g) is not closed under logspace reducibility unless we choose g = pol 1. space bounded classes [14] P = P NSPACE(log n) NSPACE(log n) P = NP, 2. bounded nondeterminism [1]: P(NPOLYLOGTIME) NPOLYLOGTIME(P) S i 0 fi i , 3. blind nondeterminism [15] ENL BNL. We were not able to achieve completeness results for the intersection emptiness problem for tally languages as it was the case for the general problem. We can, however, prove the following hardness ....

C. ` Alvarez, J. D'iaz, and J. Tor'an. Complexity classes with complete problems between P and NP-C. In Proc. of Conf. on Funfamentals of Computation Theory, number 380 in LNCS, pages 13--25. Springer, 1989.

....a polylogarithmic number of sharply bounded quantifiers. These classes would be between P and PSPACE and might yield some more concrete insight into the P = PSPACE question. A strictly nondeterministic version of this hierarchy, known as the fi hierarchy, has been studied by various researchers [2, 4, 14, 38]. A different direction would consider AQL[O(log(n) the class of relations computable in quasilinear time with O(log(n) bits of quantification but no bound on alternations. This class is still within P and contains ALOGTIME ; thus if AQL[O(log(n) 6= P then a fortiori ALOGTIME 6= P . On the ....

C. ' Alvarez, J. D'iaz, and J. Tor'an, "Complexity classes with complete problems between P and NP-complete," in Foundations of Computation Theory, Lecture Notes in Computer Science 380, Springer-Verlag, 1989, pp. 13-24.

....amounts of nondeterminism apparently needed to solve problems in NP, Kintala and Fischer [9, 10, 11] defined limited nondeterminism classes within NP, including the classes we now call the fi hierarchy. The structural properties of the fi classes were studied further by Alvarez, Diaz and Toran [1, 6]. These classes arose yet again in the work of Papadimitriou and Yannakakis [15] on particular problems inside NP (e.g. quasigroup isomorphism can be solved with O(log 2 n) nondeterministic moves) Kintala and Fischer [11] defined P f(n) to be the class of languages accepted by a ....

C. ` Alvarez, J. D'iaz and J. Tor'an, "Complexity Classes With Complete Problems Between P and NP-Complete," in Foundations of Computation Theory, Lecture Notes in Computer Science 380, Springer-Verlag, 1989, pp. 13-24.

....a polylogarithmic number of sharply bounded quantifiers. These classes would be between P and PSPACE and might yield some more concrete insight into the P = PSPACE question. A strictly nondeterministic version of this hierarchy, known as the fi hierarchy, has been studied by various researchers [2, 4, 14, 40]. A different direction would consider AQL[O(log(n) the class of relations computable in quasilinear time with O(log(n) bits of quantification but no bound on alternations. This class is still within P and contains ALOGTIME ; thus if AQL[O(log(n) 6= P then a fortiori ALOGTIME 6= P . On the ....

C. ' Alvarez, J. D'iaz, and J. Tor'an, "Complexity classes with complete problems between P and NP-complete," in Foundations of Computation Theory, Lecture Notes in Computer Science 380, Springer-Verlag, 1989, pp. 13-24.

....1 Merge(T 1 ; T 2 ; T 0 ) 0; 1 Amplify(T 0 ; T 1 ; T 2 ) 0; 1 0; 1 Append(T 1 ; 0) 00; 10 0; 1 Append(T 2 ; 1) 00; 10 01;11 Merge(T 1 ; T 2 ; T 0 ) 00;10; 01; 11 3. Bounded Nondeterminism NP computation with a limited amount of nondeterminism was introduced in [12, 13, 14] and studied further in [8, 9, 17, 7, 10, 20, 11, 5]. The class NPbits(b(n) consists of languages recognized by NP machines that make at most b(n) binary nondeterministic choices on each computation path on inputs of length n. Actually, prior treatments allowed O(b(n) binary choices, but the constant factor is very important in connection with ....

J. D. C. Alvarez and J. Toran. Complexity classes with complete problems between P and NP-complete. In Foundations of Computation Theory,pages 13--24. Springer-Verlag,1989. LNCS 380.

....D, M memory cells, and P processors, it can be simulated by his model with O(D s) PA Match operations and O(s log s D) other operations, where s = O(log PM ) 8.4. Bounded Nondeterminism NP computation with a limited amount of nondeterminism was introduced in [26] and studied further in [14, 16, 33, 13, 22, 42, 23, 9]. Definition 6. ffl An NPinit(s(n) Turing machine is an NP TM that nondeterministically chooses a number between 1 and s(n) then proceeds deterministically. ffl An NPpaths(s(n) Turing machine is an NP TM with at most s(n) paths on any length n input. ffl NPinit(s(n) is the class of ....

J. D. C. Alvarez and J. Tor'an. Complexity classes with complete problems between P and NP-complete. In Foundations of Computation Theory, pages 13--24. SpringerVerlag, 1989. LNCS 380.

....nondeterminism apparently needed to solve problems in NP, Kintala and Fischer [8, 9, 10] defined limited nondeterminism classes within NP, including the classes we now call the fi hierarchy. The structural properties of the fi classes were studied further by Alvarez, Diaz and Toran [1, 6]. These classes arose yet again in the work of Papadimitriou and Yannakakis [14] on particular problems inside NP (e.g. quasigroup isomorphism can be solved with O(log 2 n) nondeterministic moves) Kintala and Fischer [10] defined P f(n) to be the class of languages accepted by a ....

C. ` Alvarez, J. D'iaz and J. Tor'an, "Complexity Classes With Complete Problems Between P and NP-Complete," in Foundations of Computation Theory, Lecture Notes in Computer Science 380, Springer-Verlag, 1989, pp. 13-24.

....to which the fiP hierarchy has this structure. 3.1.2 Complete problems and other structural properties Properties which distinguish the fiP hierarchy and NP are known only in relativized worlds. The next two theorems show similarities between NP and classes in the fiP hierarchy. Theorem 3. 3 [2] fi k P is closed under polynomial time disjunctive reducibility, for every k 2 N . This implies that every fi k P is also closed under polynomial time and logspace many one reductions (denoted P m and L m ) It is open whether fi k P is closed under polynomial time conjunctive reducibility. ....

....k P is closed under polynomial time disjunctive reducibility, for every k 2 N . This implies that every fi k P is also closed under polynomial time and logspace many one reductions (denoted P m and L m ) It is open whether fi k P is closed under polynomial time conjunctive reducibility. In [2] this question is answered negatively in a relativized world. Theorem 3.4 (cf. 2, 12, 17, 25, 36] For every k 2 N , fi k P has L m complete sets. In [25] generic complete sets were shown to be complete for fi k P. Those sets are fi k C = fhM; x; 1 t i j M(x) accepts in t steps using ....

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C. ` Alvarez, J. D'iaz, and J. Tor'an. Complexity classes with complete problems between P and NP-C. In Proceedings Foundation of Computation Theory, pages 3--24. Lecture Notes in Computer Science #380, Springer, 1989. Journal version see [14].

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C. ` Alvarez, J. D'iaz, and J. Tor'an. Complexity classes with complete problems between P and NP-C. In Proc. of Conf. on Funfamentals of Computation Theory, number 380 in LNCS, pages 13--25. Springer, 1989.

No context found.

C. ' Alvarez, J. D'iaz, and J. Tor'an, "Complexity classes with complete problems between P and NP-complete," in Foundations of Computation Theory, Lecture Notes in Computer Science 380, Springer-Verlag, 1989, pp. 13-24.

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