Questions tagged [homomorphism]

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6
votes
1answer
168 views

Automata : Language Containment, Minimality & Graph Homomorphism

Given two DFAs $A$ and $B$ defined on the same alphabet, a (graph) homomorphism $h:A \rightarrow B$ from $A$ to $B$ is a mapping of the states of $A$ into the states of $B$ such that : if the state $...
16
votes
0answers
282 views

Complexity of the homomorphism problem parameterized by treewidth

The homomorphism problem $\text{Hom}(\mathcal{G}, \mathcal{H})$ for two classes $\mathcal{G}$ and $\mathcal{H}$ of graphs is defined as follows: Input: a graph $G$ in $\mathcal{G}$, a graph $H$ in $...
9
votes
1answer
227 views

Complexity of digraph homomorphism to an oriented cycle

Given a fixed directed graph (digraph) $D$, the $D$-COLORING decision problem asks whether an input digraph $G$ has a homomorphism to $D$. (A homomorphism of $G$ to $D$ is a mapping $f$ of $V(G)$ to $...
10
votes
0answers
101 views

Chomsky-Schützenberger for Deterministic CFLs

Is there a Chomsky-Schützenberger representation theorem for deterministic CFLs? Knowing precisely the class of morphisms under which DCFL is closed, such a theorem would probably be of the form: $...
5
votes
1answer
138 views

When does automaton stay unchanged after string homomorphism?

Suppose we have a string homomorphism $\varphi: \Sigma \rightarrow \Sigma^*$. Consider the languages in $\varphi(\Sigma^*)$ whose letters are elements of $\varphi(\Sigma)$, so here I do not want to ...
9
votes
1answer
182 views

Complexity of counting graph endomorphisms

A homomorphism from a graph $G = (V, E)$ to a graph $G' = (V', E')$ is a mapping $f$ from $V$ to $V'$ such that if $x$ and $y$ are adjacent in $E$ then $f(x)$ and $f(y)$ are adjacent in $E'$. An ...
2
votes
2answers
128 views

Polynomial time construction of families of pairwise nonhomomorphic graphs

Is it true that for all $n$ there are $n$ pairwise nonhomomorphic graphs with $poly(n)$ vertices? Is there a polynomial time algorithm for constructing such families of graphs?