We examine visibly counter languages, which are languages recognized by visibly counter automata (a.k.a. input driven counter automata). We are able to effectively characterize the visibly counter languages in AC0, and show that they are contained in FO[+].
more >>>In the setting known as DLOGTIME-uniformity,
the fundamental complexity classes
$AC^0\subset ACC^0\subseteq TC^0\subseteq NC^1$ have several
robust characterizations.
In this paper we refine uniformity further and examine the impact
of these refinements on $NC^1$ and its subclasses.
When applied to the logarithmic circuit depth characterization of $NC^1$,
some refinements leave ...
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We show that every language accepted by a nondeterministic auxiliary pushdown automaton in polynomial time (that is, every language in SAC$^1$ = LogCFL) can be accepted by a symmetric auxiliary pushdown automaton in polynomial time.
We present a deterministic algorithm running in space
O((log^2 n)/loglog n) solving the connectivity problem
on strongly unambiguous graphs. In addition, we present
an O(log n) time-bounded algorithm for this problem
running on a parallel pointer machine.
