F. Cucker, M. Matamala, On digital nondeterminism, Mathematical Systems Theory 29 (1996) 635--647. Home/Search Document Not in Database Summary Related Articles Check |
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Polynomials of Bounded Tree-Width - Makowsky, Meer (2000) (Correct)
....be reduced to (4; 1) Gamma FEASR (A) for jAj 2: This includes for example the real Knapsack problem and, of course, also the classical SAT problem. It is therefore reasonable considering (4; 1) Gamma FEASR (A) to be a difficult problem in the BSS setting. Complete problems for DNPR do exist ([CucMat]) Our first main theorem is Theorem 9. For finite fields F of size f the problems (d; k) Gamma FEASF and (d; k) Gamma HNF can be solved in time O(n) where the constant depends on k; d; f . The same holds for finite rings. The proof exploits the finiteness of the field (ring) by making all ....
F. Cucker, M. Matamala. On digital nondeterminism. Mathematical Systems Theory, 29:635--647, 1996.
Polynomials of Bounded Tree Width (Extended Abstract) - Makowsky, Meer (2000) (Correct)
....following variation of our problems. De nition 5. Given a set of n polynomial inequalities P of degree d and of tree width at most k in n variables over the reals and A R a nite set. d; k) P IS(A)R : Does P have a solution in A n The following partial result can easily be obtained from [Poi95,CM96] Proposition 1. d; 1) P IS(A)R is DNPR complete over the reals for d 2. Theorem 7. For nite elds F of size q, d; k) FEAS F and (d; k) HN F can be solved in time O(n) where the constant depends on k; d; q. The same holds for nite rings. The proof exploits the niteness of the eld (ring) ....
F. Cucker and M. Matamala. On digital nondeterminism. Mathematical Systems Theory, 29:635-647, 1996.
Reductions to Sets of Low Information Content.. - Arvind, Han.. (Correct)
....UP, PP, and C= P. Since for every set A 2 UP it holds that Left(A) is in UP, it also follows that if UP is contained in R p bc (R p 1 tt (R p c (SPARSE) then UP = P. This strengthens the 4 The left set tacitly depends on the particular witness relation chosen. 6 results of Watanabe [Wat91] who showed that if P 6= UP then there exists a set in UP that does not many one polynomial time reduce to any sparse set. Consider the set fhx; mi fi fi there are at least m satisfying assignments for xg, which has properties similar to left sets and is complete for PP. Under the assumption ....
O. Watanabe. On intractability of the class UP. Mathematical Systems Theory, 24:1--10, 1991.
On Some Promise Classes in Structural Complexity Theory - Rothe (Correct)
....thesis. In particular, we study to what extent, if any, results for the thoroughly investigated non promise class NP carry over to the promise classes UP and FewP. The study of UP is crucial in both cryptography and structural complexity theory. There has been a long line of research regarding UP [Val76, Rac82, GS88, HH88, HH91, Wat88, Wat91]. To pinpoint some of the most important results about UP, we mention the following. Grollmann and Selman [GS88] have shown that one way functions exist if and only if P 6= UP. Informally speaking, a one way function is one that is easy to compute but hard to invert. It is not known whether UP ....
O. Watanabe. On intractability of the class UP. Mathematical Systems Theory, 24:1--10, 1991.
Reductions to Sets of Low Information Content - Arvind, Han, Hemachandra.. (1993) (21 citations) (Correct)
....sets (see [AKM] We now briefly discuss the application of the above results to the classes UP, PP and C= P. Since for every set A 2 UP it holds that Lef t(A) is in UP, it also follows that if UP is contained in R p b (R p c (SPARSE) then P = UP. This strengthens the results of Watanabe [Wat91] who showed that if P 6= UP then there exists a set in UP that does not many one polynomial time reduce to any sparse set. Consider the set fhx; mi fi fi fi there are at least m satisfying assignments for xg, which has properties similar to left sets and is complete for PP. Under the assumption ....
O. Watanabe. On intractability of the class UP. Mathematical Systems Theory, 24:1--10, 1991.
Multi-Linear Formulas for Permanent and Determinant are of.. - Raz (2003) (3 citations) Self-citation (Formulas) (Correct)
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E. Shamir, M. Snir. On the Depth Complexity of Formulas. Mathematical Systems Theory 13: 301-322 (1980)
Discrete versus Analog Computation: Aspects of Studying the Same.. - Meer (1998) (Correct)
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F. Cucker, M. Matamala, On digital nondeterminism, Mathematical Systems Theory 29 (1996) 635--647.
Polynomials of Bounded Tree-Width - Makowsky, Meer (2000) (Correct)
No context found.
F. Cucker, M. Matamala. On digital nondeterminism. Mathematical Systems Theory, 29:635--647, 1996.
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