电路可满足性问题的多项式时间启发式算法

布尔电路的启发式优化及其在基于属性的加密中的应用

Heuristics Optimization of Boolean Circuits with application in Attribute Based Encryption

本文提出六种启发式算法优化单调布尔电路，通过重写为等价简单形式，提升基于属性的加密（ABE）方案中布尔电路的性能，并验证了独立及集成优化效果。

Lower Bounds Against Sparse Symmetric Functions of ACC Circuits: Expanding the Reach of $\#$SAT Algorithms

We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in $\text{Quasi-NP} = \text{NTIME}[n^{(\log n)^{O(1)}}]$ and $\text{NEXP}$ do not have small circuits from various circuit classes ${\cal C}$, by showing that ${\cal C}$ admits non-trivial satisfiability and/or $\#$SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of non-trivial $\#$SAT algorithm for a circuit class ${\mathcal C}$. Say a symmetr…

随机3-可满足性回溯求解的启发式平均-实例分析

Heuristic average-case analysis of the backtrack resolution of random 3-Satisfiability instances

分析了回溯算法求解随机3-可满足性（SAT）实例的平均情况复杂度。我们首先解释以前的严格的工作在一个统一的框架的基础上的统计物理概念的动力学轨迹，相图和生长过程。在DPLL算法的作用下，3-SAT实例被转化为2+p-SAT实例，其特征参数（子句与变量之比α，3-子句的分数p）可以在运算过程中被跟踪，并定义了解析轨迹.根据轨迹在2+p-SAT模型相图中的位置，生成简单（多项式）或困难（指数）分辨率。三个政权被确定，这取决于比率α的3-SAT的实例来解决。较低的饱和阶段：对于小的比率，DPLL几乎肯定会在随着变量数量N线性增长的时间内找到解决方案。饱和期上限：对于中间比率，实例几乎肯定是可满足的，但找到解需要高概率的指数时间（2 ^（N Ω），Ω>0）。非饱和阶段：对于大的比率，几乎总是没有解，反驳的证明是指数的。分析的增长的搜索树在上sat和unsat制度，并允许我们估计欧米茄作为一个函数的α。这种分析是基于搜索树的平均大小和编码搜索启发式的基本步骤的进化算子的功率之间的精确关系。

Deterministic Algorithms for Compiling Quantum Circuits with Recurrent Patterns

Current quantum processors are noisy, have limited coherence and imperfect gate implementations. On such hardware, only algorithms that are shorter than the overall coherence time can be implemented and executed successfully. A good quantum compiler must translate an input program into the most efficient equivalent of itself, getting the most out of the available hardware. In this work, we present novel deterministic algorithms for compiling recurrent quantum circuit patterns in polynomial time. In particular, such patterns appear in quantum circuits that are used to compute the ground state p…

Simulating Quantum Computations with Tutte Polynomials

We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic matroids. The algorithm evaluates the Tutte polynomial recursively using the deletion-contraction property while attempting to exploit structural properties of the matroid. We consider several variations of our algorithm and present experimental results comparing their performance on two classes of random quantum circuits. Further, we obtain an explicit form for Cl…

Circuit Satisfiability Problem for circuits of small complexity

The following problem is considered. A Turing machine $M$, that accepts a string of fixed length $t$ as input, runs for a time not exceeding a fixed value $n$ and is guaranteed to produce a binary output, is given. It's required to find a string $X$ such that $M(X) = 1$ effectively in terms of $t$, $n$, the size of the alphabet of $M$ and the number of states of $M$. The problem is close to the well-known Circuit Satisfiability Problem. The difference from Circuit Satisfiability Problem is that when reduced to Circuit Satisfiability Problem, we get circuits with a rich internal structure (in p…