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\documentclass{acmabs}
\begin{document}
\Journal{Journal of the ACM}
\refkey{CourcoubetisY95}
\title{The Complexity of Probabilistic Verification}
\author{Costas Courcoubetis \and Mihalis Yannakakis}
\Pages{857--907}
\Month{July}
\Year{1995}
\Volume{42}
\Number{4}
\maketitle
\begin{abstract}
We determine the complexity of testing whether a finite state, sequential or
concurrent probabilistic program satisfies its specification expressed in
linear time temporal logic. For sequential programs we present an algorithm
that runs in time linear in the program and exponential in the specification,
and also show that the problem is in PSPACE, matching the known lower bound.
For concurrent programs we show that the problem can be solved in time
polynomial in the program and doubly exponential in the specification, and
prove that it is complete for double exponential time. We also address these
questions for specifications described by $\omega$-automata or formulas in
extended temporal logic.
\end{abstract}
\begin{categories}
D.2.4; F.2.2 [complexity of proof procedures]; F.3.1 [mechanical verification];
G.3 [probabilistic algorithms]
\end{categories}
\begin{terms}
Algorithms, Theory, Verification
\end{terms}
\begin{keywords}
Automata, EXPTIME-complete, Markov chain, model checking, probabilistic
algorithm, PSPACE-complete, temporal logic
\end{keywords}
\end{document}