  Given a text and a pattern over an alphabet, the pattern matching problem
searches for all occurrences of the pattern in the text. An equivalence
relation $\approx$ is called a substring consistent equivalence relation
(SCER), if for two strings $X$ and $Y$, $X \approx Y$ implies $|X| = |Y|$ and
$X[i:j] \approx Y[i:j]$ for all $1 \le i \le j \le |X|$. In this paper, we
propose an efficient parallel algorithm for pattern matching under any SCER
using the"duel-and-sweep" paradigm. For a pattern of length $m$ and a text of
length $n$, our algorithm runs in $O(\xi_m^\mathrm{t} \log^2 m)$ time and
$O(\xi_m^\mathrm{w} \cdot n \log^2 m)$ work, with $O(\tau_n^\mathrm{t} +
\xi_m^\mathrm{t} \log^2 m)$ time and $O(\tau_n^\mathrm{w} + \xi_m^\mathrm{w}
\cdot m \log^2 m)$ work preprocessing on the Priority Concurrent Read
Concurrent Write Parallel Random-Access Machines (P-CRCW PRAM).
