On efficiency of notations for natural numbers
Computing a function on natural numbers assumes a fixed notation for natural numbers. Usually, we assume the binary or decimal notation. However, different notations might have different sets of effectively (PTIME) computable ...
Highlights
- Among all dense notations for natural numbers, positional notations allow to compute in PTIME a maximal set of functions.
Weighted 2-sections and hypergraph reconstruction
In the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems:
- Given a weighted ...
On the complexity of and solutions to the minimum stopping and trapping set problems
In this paper, we discuss the problems of finding minimum stopping sets and trapping sets in Tanner graphs, using integer linear programming. These problems are important for establishing reliable communication across noisy channels. ...
Completeness, approximability and exponential time results for counting problems with easy decision version
- The first TotP-complete problems under parsimonious reductions.
- Hardness of ...
Hard counting problems with easy decision version, like computing the permanent and counting independent sets, are of particular importance in counting complexity theory. TotP is the class of all self-reducible problems in # P with ...
Universal product learning with errors: A new variant of LWE for lattice-based cryptography
The middle product learning with errors problem (MP-LWE) is a variant of the learning with errors problem (LWE). The public-key cryptography under MP-LWE assumption gets an equilibrium between “efficiency” and “security”. However, the ...
