Related papers: A Satisfiability Algorithm for AC$^0$
We apply in this article (non rigorous) statistical mechanics methods to the problem of counting long circuits in graphs. The outcomes of this approach have two complementary flavours. On the algorithmic side, we propose an approximate…
Randomized compiling (RC) is an efficient method for tailoring arbitrary Markovian errors into stochastic Pauli channels. However, the standard procedure for implementing the protocol in software comes with a large experimental overhead --…
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Recent years have seen renewed attention to arithmetic coding (AC). This is thanks to the use of AC for distribution matching (DM) to control the channel input distribution in probabilistic amplitude shaping. There are two main problems…
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Incorporating the AC power flow equations into unit commitment models has the potential to avoid costly corrective actions required by less accurate power flow approximations. However, research on unit commitment with AC power flow…
We give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of $\text{pw}(G)+1$, where $\text{pw}(G)$ is the pathwidth of $G$. Starting from a path decomposition, the algorithm runs in $O(nm)$ time,…
A key problem in constrained random verification (CRV) concerns generation of input stimuli that result in good coverage of the system's runs in targeted corners of its behavior space. Existing CRV solutions however provide no formal…
Relaxing the sequential specification of a shared object is a way to obtain an implementation with better performance compared to implementing the original specification. We apply this approach to the Counter object, under the assumption…
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our…
In this work, we prove the strongest known lower bounds for QAC$^0$, allowing polynomially many gates and ancillae. Our main results show that: (1) Depth-3 QAC$^0$ circuits cannot compute PARITY, and require $\Omega(\exp(\sqrt{n}))$ gates…
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