P. Koiran. The real dimension problem is NPR -complete. LIP Research Report 97-36, Ecole Normale Sup'erieure de Lyon, 1997. Home/Search Document Details and Download
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Report for Publication of the Activity of the Working Group.. - Shawe-Taylor (1997) (Correct)
....study of the power of analog neural nets. A basic result was given by Koiran [25] Further research is in [13, 14, 23] 2. Characterize the power of randomization. The papers [12, 22] give precise results in this direction. 3. Characterize the complexity of some computational problems. Papers [24, 26, 27] are important recent results. 4. Characterize complexity classes by means of logic. This research line in continuous computation was initiated in the paper [17] Further developments are contained in [15] 5. Prove the equivalence of different models of continuous computation, in order to ....
P. Koiran, The real dimension problem is NPR -complete.
The Real Dimension Problem is NPR-Complete - Koiran (1997) (1 citation) Self-citation (Koiran) (Correct)
....in the classical (bit cost) complexity. We show that the corresponding problems (4FEAS and DIM) can be reduced to each other in polynomial time. Finally, the randomized and deterministic complexity of DIMR is touched upon in section 5. A preliminary version of this paper can be found in [14]. 1.1 Representation of semi algebraic sets Our results have very little dependence on the choice of a representation for semi algebraic sets. It is customary to represent them as unions of basic semialgebraic sets of the form P 1 (x) Delta 1 0; Delta Delta Delta ; Pm (x) Delta m 0 (1) ....
P. Koiran. The real dimension problem is NPR -complete. LIP Research Report 97-36, Ecole Normale Sup'erieure de Lyon, 1997.
Elimination of Parameters in the Polynomial Hierarchy - Koiran (1998) Self-citation (Koiran) (Correct)
....such that K j= F (v) whenever p(v) 6= 0. One could also define a 8 quantifier as: 8 v F (v) j :9 v :F (v) but this would be redundant since this double negation is equivalent to 9 v F (v) Note however that in real closed fields, one can similarly define two distinct quantifiers 9 and 8 [15]. First order formulas involving this new quantifier will be called generalized formulas . Ordinary formulas will just be referred to as formulas , or firstorder formulas . This distinction will be dropped shortly since, as we now show, generalized formulas are equivalent to ordinary ....
....to convert automatically an MA or an AM algorithm into an NP algorithm. In particular, this may yield an optimal algorithm if the problem under consideration is NPK hard. See [14] for an example of a conversion of an AM algorithm into an NP algorithm. Also the NPR completeness result of [15] can be seen as a conversion of an MA algorithm over the reals into an NP algorithm. 5.3 Boolean Parts Let K be an algebraically closed field of characteristic 0. We recall that the boolean part BP(NPK ) of NPK is the set of boolean problems (subsets of f0; 1g 1 ) that belong to NPK . ....
P. Koiran. The real dimension problem is NPR -complete. LIP Research Report 97-36, Ecole Normale Sup'erieure de Lyon, 1997.
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