A Uniform Circuit Lower Bound for the Permanent
ثبت نشده
چکیده
the new circuit consists of a subexponential number of circuits, each of which is of subex-ponential size, the new circuit is also of subexponential size. The depth of the new circuit family is the same as fC n g but the top layer of MOD p gates has been \absorbed" into the symmetric gate computing B and been replaced by a layer of AND gates of small fan-in. Now, by an appeal to Lemma 9, the circuit can be converted into nice form, which completes the proof. (of Theorem 3) By Lemma 16, every language in ACC(subexp) is accepted by a deterministic SYMACC circuit family of subexponential size, with small fan-in AND gates, no OR gates, and no MOD m gates for composite m. Successive applications of Lemma 17 and Lemma 18 remove all MOD gates from the circuit, while maintaining the property that all AND gates have small fan-in. This suces to prove the theorem.
منابع مشابه
A Uniform Circuit Lower Bound for the Permanent
We show that uniform families of ACC circuits of subexponential size cannot compute the permanent function. This also implies similar lower bounds for certain sets in PP. This is one of the very few examples of a lower bound in circuit complexity where the uniformity condition is essential; it is still unknown if there is any set in Ntime (2 n O(1) ) that does not have nonuniform ACC circuits.
متن کاملA Uniform Circuit Lower Bound for the Permanent Eric Allender and Vivek Gore
We show that uniform families of ACC circuits of subexponential size cannot compute the permanent function. This also implies similar lower bounds for certain sets in PP. This is one of the very few examples of a lower bound in circuit complexity whose proof hinges on the uniformity condition; it is still unknown if there is any set in Ntime (2 O(1) ) that does not have nonuniform ACC circuits.
متن کاملThe Permanent Requires Large Uniform Threshold Circuits
We show that the permanent cannot be computed by uniform constantdepth threshold circuits of size T (n), for any function T such that for all k, T (n) = o(2). More generally, we show that any problem that is hard for the complexity class C=P requires circuits of this size (on the uniform constant-depth threshold circuit model). In particular, this lower bound applies to any problem that is hard...
متن کاملAn exponential lower bound for homogeneous depth four arithmetic circuits with bounded bottom fanin
Agrawal and Vinay [AV08] have recently shown that an exponential lower bound for depth four homogeneous circuits with bottom layer of × gates having sublinear fanin translates to an exponential lower bound for a general arithmetic circuit computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via homogeneous depth four circuits with boun...
متن کاملA Novel Technique on the Analytical Calculation of Open-Circuit Flux Density Distribution in Brushless Permanent-Magnet Motor
Both the cogging and electromagnetic torques depends on the shape of the flux density distribution in the airgap region. A two-dimensional (2-D) analytical method for predicting the open- circuit airgap field distribution in brushless permanent magnet motors, considering the direction of magnetization, i.e., radial or parallel, and the effect of real shape of stator slot-openings is presented i...
متن کاملLower Bounds against Weakly Uniform Circuits
A family of Boolean circuits {Cn}n>0 is called γ(n)-weakly uniform if there is a polynomial-time algorithm for deciding the directconnection language of every Cn, given advice of size γ(n). This is a relaxation of the usual notion of uniformity, which allows one to interpolate between complete uniformity (when γ(n) = 0) and complete nonuniformity (when γ(n) > |Cn|). Weak uniformity is essential...
متن کامل