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- Jin-Yi Cai, Zhiguo Fu
- STOC
- 2017

We prove a complexity classification theorem that classifies all counting constraint satisfaction problems (#CSP) over Boolean variables into exactly three classes: (1) Polynomial-time solvable; (2) #P-hard for general instances, but solvable in polynomial-time over planar structures; and (3) #P-hard over planar structures. The classification applies to all… (More)

- Jin-Yi Cai, Zhiguo Fu
- Inf. Comput.
- 2014

Holographic algorithms with matchgates are a novel approach to design polynomial time computation. It uses Kasteleyn's algorithm for perfect matchings, and more importantly a holographic reduction. The two fundamental parameters of a holographic reduction are the domain size k of the underlying problem, and the basis size ℓ. A holographic reduction… (More)

- Jin-Yi Cai, Zhiguo Fu, Heng Guo, Tyson Williams
- 2015 IEEE 56th Annual Symposium on Foundations of…
- 2015

We prove a complexity dichotomy for complex-weighted Holant problems with an arbitrary set of symmetric constraint functions on Boolean variables. In the study of counting complexity, such as #CSP, there are problems which are #P-hard over general graphs but P-time solvable over planar graphs. A recurring theme has been that a holographic reduction [36] to… (More)

- Heng Guo, Andreas Galanis, +6 authors Wentao Wu
- 2016

- Jin-Yi Cai, Zhiguo Fu, Mingji Xia
- ArXiv
- 2017

We prove a complexity dichotomy theorem for the six-vertex model. For every setting of the parameters of the model, we prove that computing the partition function is either solvable in polynomial time or #P-hard. The dichotomy criterion is explicit.

- Zhiguo Fu, Fengqin Yang
- Inf. Process. Lett.
- 2014

An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized by matchgates under a suitable basis transformation (SRP). For holographic algorithms on domain size 2, [1, 2, 4, 5] have built a systematical theory. In this paper, we reduce SRP on domain size k ≥ 3 to SRP on domain size 2 for… (More)

- Zhiguo Fu, Xi Zhang, Yaohua Shi, Qirong Dong
- Medical science monitor : international medical…
- 2016

BACKGROUND This study aimed to compare the surgical outcomes between open pedicle screw fixation (OPSF) and percutaneous pedicle screw fixation (PPSF) for the treatment of thoracolumbar fractures, which has received scant research attention to date. MATERIAL AND METHODS Eight-four patients with acute and subacute thoracolumbar fractures who were treated… (More)

- Jin-Yi Cai, Zhiguo Fu, Shuai Shao
- ArXiv
- 2017

We prove a complexity classification theorem that divides the six-vertex model into exactly three types. For every setting of the parameters of the model, the computation of the partition function is precisely: (1) Solvable in polynomial time for every graph, or (2) #P-hard for general graphs but solvable in polynomial time for planar graphs, or (3) #P-hard… (More)

- Zhiguo Fu
- ArXiv
- 2017

For any n ≥ 3 and q ≥ 3, we prove that the Equality function (=n) on n variables over a domain of size q cannot be realized by matchgates under holographic transformations. This is a consequence of our theorem on the structure of blockwise symmetric matchgate signatures. This has the implication that the standard holographic algorithms based on matchgates,… (More)

- Jin-Yi Cai, Zhiguo Fu
- ArXiv
- 2017

We prove a complexity dichotomy theorem for the eight-vertex model. For every setting of the parameters of the model, we prove that computing the partition function is either solvable in polynomial time or #P-hard. The dichotomy criterion is explicit. For tractability, we find some new classes of problems computable in polynomial time. For #P-hardness, we… (More)