COMPLEXITY OF SHORT GENERATING FUNCTIONS
Copyright policy )COMPLEXITY OF SHORT GENERATING FUNCTIONS
We give complexity analysis for the class ofshort generating functions. Assuming#P$\not \subseteq$FP/poly, we show that this class is not closed under taking many intersections, unions or projections of generating functions, in the sense that these operations can increase the bit length of coefficients of generating functions by a super-polynomial factor. We also prove thattruncated theta functionsare hard for this class.
- University of California, Los Angeles United States
68Q15 (secondary), FOS: Computer and information sciences, Computer Science - Logic in Computer Science, 68Q17 (primary), Discrete Mathematics (cs.DM), Exact enumeration problems, generating functions, Mathematics - Logic, Computational Complexity (cs.CC), Logic in Computer Science (cs.LO), Computer Science - Computational Complexity, QA1-939, FOS: Mathematics, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Complexity classes (hierarchies, relations among complexity classes, etc.), Mathematics - Combinatorics, Combinatorics (math.CO), Logic (math.LO), Mathematics, Computer Science - Discrete Mathematics
68Q15 (secondary), FOS: Computer and information sciences, Computer Science - Logic in Computer Science, 68Q17 (primary), Discrete Mathematics (cs.DM), Exact enumeration problems, generating functions, Mathematics - Logic, Computational Complexity (cs.CC), Logic in Computer Science (cs.LO), Computer Science - Computational Complexity, QA1-939, FOS: Mathematics, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Complexity classes (hierarchies, relations among complexity classes, etc.), Mathematics - Combinatorics, Combinatorics (math.CO), Logic (math.LO), Mathematics, Computer Science - Discrete Mathematics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!