Variations on Muchnik’s Conditional Complexity Theorem
Muchnik’s theorem about simple conditional descriptions states that for all strings a and b there exists a program p transforming a to b that has the least possible length and is simple conditional on b. In this paper we present two new proofs of this ...
On the Complexity of Matroid Isomorphism Problem
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in $\Sigma_{2}^{p}$. In the case of linear matroids, which are represented over polynomially growing fields, we note that the problem is unlikely ...
New Plain-Exponential Time Classes for Graph Homomorphism
A homomorphism from a graph G to a graph H (in this paper, both simple, undirected graphs) is a mapping f:V(G)→V(H) such that if uv∈E(G) then f(u)f(v)∈E(H). The problem Hom (G,H) of deciding whether there is a homomorphism is NP-complete, and in fact ...
Compressed Word Problems in HNN-extensions and Amalgamated Products
It is shown that the compressed word problem for an HNN-extension 〈H,t∣t −1 at=ϕ(a) (a∈A)〉 with A finite is polynomial time Turing-reducible to the compressed word problem for the base group H. An analogous result for amalgamated free products is shown ...
Concatenation of Regular Languages and Descriptional Complexity
We investigate the deterministic and nondeterministic state complexity of languages resulting from the concatenation of two regular languages represented by deterministic and nondeterministic finite automata. We prove that the whole range of ...
One-Nonterminal Conjunctive Grammars over a Unary Alphabet
Conjunctive grammars over an alphabet Σ={a} are studied, with the focus on the special case with a unique nonterminal symbol. Such a grammar is equivalent to an equation X=ϕ(X) over sets of natural numbers, using union, intersection and addition. It is ...
Lower Bounds for the Determinantal Complexity of Explicit Low Degree Polynomials
The determinantal complexity of a polynomial f(x 1,x 2,…,x n ) is the minimum m such that f=det m (L(x 1,x 2,…,x n )), where L(x 1,x 2,…,x n ) is a matrix whose entries are affine forms in the x i s over some field $\mbox {$\mathbb {F}$}$.
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Unique Decipherability in the Monoid of Languages: An Application of Rational Relations
We attack the problem of deciding whether a finite collection of finite languages is a code, that is, possesses the unique decipherability property in the monoid of finite languages. We investigate a few subcases where the theory of rational relations ...
Querying Data Sources that Export Infinite Sets of Views
We study the problem of querying data sources that accept only a limited set of queries, such as sources accessible by Web services which can implement very large (potentially infinite) families of queries. We revisit a classical setting in which the ...
Containment of Conjunctive Queries on Annotated Relations
We study containment and equivalence of (unions of) conjunctive queries on relations annotated with elements of a commutative semiring. Such relations and the semantics of positive relational queries on them were introduced in a recent paper as a ...
Reconcilable Differences
In this paper we study a problem motivated by the management of changes in databases. It turns out that several such change scenarios, e.g., the separately studied problems of view maintenance (propagation of data changes) and view adaptation (...
Query Languages for Data Exchange: Beyond Unions of Conjunctive Queries
The class of unions of conjunctive queries (UCQ) has been shown to be particularly well-behaved for data exchange; its certain answers can be computed in polynomial time (in terms of data complexity). However, this is not the only class with this ...
