UNIQUE SAT is the problem of deciding whether a given Boolean formula has exactly one satisfying truth assignment. This problem is a typical (moreover complete) representative of a natural class of problems about unique solutions. All these problems belong to the class DIFe= {L1--L2:L1,Lz~NP} studied by Papadimitriou and Yannakakis. We consider the relationship between these two classes, partic...

Though integer factorization and discrete logarithm problem are both practically and theoretically important, the computational complexity of these problems remained unknown. By comparing integer factorization problem with a problem in P and NP-complete problems, I show that the decision problem version of integer factorization problem is neither in P nor NP-complete. In addition, integer facto...

The analysis discussed in this paper is based on a well-known NP-complete problem which is called “satisfiability problem or SAT”. From SAT a new NP-complete problem is derived, which is described by a Boolean function called “core function”. In this paper it is proved that the cost of the minimal implementation of core function increases with n exponentially. Since the synthesis of core functi...

We study the Minimum Circuit Size Problem (MCSP): given the truth-table of a Boolean function f and a number k, does there exist a Boolean circuit of size at most k computing f? This is a fundamental NP problem that is not known to be NP-complete. Previous work has studied consequences of the NP-completeness of MCSP. We extend this work and consider whether MCSP may be complete for NP under mor...

It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3-connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $O(n)$ time.

The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195200) proved that the Hamiltonian Cycle Problem is NP-Complete even for undirected path graphs and left the Hamiltonian cycle problem open for directed path graphs. Narasimhan (1989, Information Processing Letters, 32, 167-170) proved tha...