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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 [Val08] to FKT precisely captures these problems...
The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this paper, we prove a decidable complexity dichotomy theorem for this problem and our theorem applies to all non-negative weighted form of the problem: given any fixed...
Intelligent testing paper generation system is a matter of multi-objective optimization, and high-quality testing papers can be made by setting more detailed properties of examination questions. This paper designs some implementation strategies to satisfy users' testing requests, such as establishing knowledge points testing area and the proportions of each knowledge point as well as their requests...
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