We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then apply the partially ordered sets to Coxeter groups. Some results are a proof that enumerating the reduced words of elements of Coxeter groups is #P-complete, a ...

The problem of determining the size of a finite concept lattice is shown to be #P-complete. Since any finite lattice can be represented as a concept lattice, the problem of determining the size of a lattice given by the ordered sets of its irreducibles is also #P-complete. Some results about NP-completeness or polynomial tractability of decision problems related to concepts with bounded extent,...

What kind of operations can we perform effectively (without full unpacking) with compressed texts? In this paper we consider three fundamental problems: (1) check the equality of two compressed texts, (2) check whether one compressed text is a substring of another compressed text, and (3) compute the number of different symbols (Hamming distance) between two compressed texts of the same length....

The complexity of calculating the coefficients of the Tutte polynomial of a graph is considered. The calculation of some coefficients is shown to be # P-complete, whereas some other coefficients can be computed in polynomial time. However, even for a hard coefficient, it can be decided in polynomial time whether it is less than a fixed constant.

Recently, there has been much interest in studying certain graph partitions that generalize graph colourings and homomorphisms. They are described by a pattern, usually viewed as a symmetric {0, 1, ∗}matrix M . Existing results focus on recognition algorithms and characterization theorems for graphs that admit such M -partitions, or M partitions in which vertices of the input graph G have lists...

A model of learning from positive and negative examples in concept lattices is considered. Latticeand graph-theoretic interpretations of learning concept-based classi0cation rules (called hypotheses) and classi0cation in this model are given. The problems of counting all formal concepts, all hypotheses, and all minimal hypotheses are shown to be #P-complete. NP-completeness of some decision pro...

We consider the complexity of the emptiness problem for various classes of graph languages deened by eNCE (edge label neighborhood controlled embedding) graph grammars. In particular, we show that the emptiness problem is undecidable for general eNCE graph grammars, DEXPTIME-complete for connuent and boundary eNCE graph grammars, PSPACE-complete for linear eNCE graph grammars, NL-complete for d...

Let M be the polynomial-time TM and p be the polynomial bound such that f(x) = #{y ∈ {0, 1}p(|x|) | M(x, y) = 1}. Define M ′(x,N, y′) for N a length p(|x|) binary string viewed as an integer and |y′| = p(|x|) + 1 by M ′(x,N, 0y) = M(x, y) and M ′(x,N, 1y) = 1 iff y ≥ N . Note that there will be precisely 2p(|x|) − N strings y′ = 1y such that M ′(x,N, y′) accepts. Therefore f(x) > N if and only ...