The present work studies clustering from an abstract point of view
and investigates its properties in the framework of inductive inference.
Any class $S$ considered is given by a numbering
$A_0,A_1,...$ of nonempty subsets of the natural numbers
or the rational k-dimensional vector space as a hypothesis space.
A clustering ... more >>>

Presented is an algorithm (for learning a subclass of erasing regular
pattern languages) which
can be made to run with arbitrarily high probability of
success on extended regular languages generated by patterns
$\pi$ of the form $x_0 \alpha_1 x_1 ... \alpha_m x_m$
for unknown $m$ but known $c$,
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A recursive enumerator for a function $h$ is an algorithm $f$ which
enumerates for an input $x$ finitely many elements including $h(x)$.
$f$ is an $k(n)$-enumerator if for every input $x$ of length $n$, $h(x)$
is among the first $k(n)$ elements enumerated by $f$.
If there is a $k(n)$-enumerator for ... more >>>

Pin & Weil [PW95] characterized the automata of existentially
first-order definable languages. We will use this result for the following
characterization of the complexity class NP. Assume that the
Polynomial-Time Hierarchy does not collapse. Then a regular language
L characterizes NP as an unbalanced polynomial-time leaf language
if and ... more >>>

Rice's Theorem says that every nontrivial semantic property
of programs is undecidable. It this spirit we show the following:
Every nontrivial absolute (gap, relative) counting property of circuits
is UP-hard with respect to polynomial-time Turing reductions.

The paper analyzes in terms of polynomial time many-one reductions
the computational complexity of several natural equivalence
relations on Boolean functions which derive from replacing
variables by expressions. Most of these computational problems
turn out to be between co-NP and Sigma^p_2.