We propose a framework for the exact probabilistic
analysis of window-based pattern matching algorithms, such as
Boyer--Moore, Horspool, Backward DAWG Matching, Backward Oracle
Matching, and more. In particular, we develop an algorithm that
efficiently computes the distribution of a pattern matching
algorithm's running time cost (such as the number of text character
accesses) for any given pattern in a random text model. Text models
range from simple uniform models to higher-order Markov models or
hidden Markov models (HMMs). Furthermore, we provide an algorithm to
compute the exact distribution of \emph{differences} in running time
cost of two pattern matching algorithms. Methodologically, we use
extensions of finite automata which we call \emph{deterministic
arithmetic automata} (DAAs) and \emph{probabilistic arithmetic
automata} (PAAs)~\cite{Marschall2008}. Given an algorithm, a
pattern, and a text model, a PAA is constructed from which the
sought distributions can be derived using dynamic programming. To
our knowledge, this is the first time that substring- or
suffix-based pattern matching algorithms are analyzed exactly by
computing the whole distribution of running time cost.
Experimentally, we compare Horspool's algorithm, Backward DAWG
Matching, and Backward Oracle Matching on prototypical patterns of
short length and provide statistics on the size of minimal DAAs for
these computations
