Computing Expected Runtimes for Constant Probability Programs

Abstract

We introduce the class of constant probability (CP) programs and show that classical results from probability theory directly yield a simple decision procedure for (positive) almost sure termination of programs in this class. Moreover, asymptotically tight bounds on their expected runtime can always be computed easily. Based on this, we present an algorithm to infer the exact expected runtime of any CP program.

Automated Termination Analysis of Polynomial Probabilistic Programs

“…We present our experimental results by separating our benchmarks within three categories: (i) 21 programs which are PAST (Table 1), (ii) 11 programs which are AST (Table 2) but not necessarily PAST, and (iii) 6 programs which are not AST ( Table 3). The benchmarks have either been introduced in the literature on probabilistic programming [42,10,4,22,38], are adaptations of well-known stochastic processes or have been designed specifically to test unique features of AMBER, like the ability to handle polynomial real arithmetic.…”

“…With these criteria, 10 out of the 50 original benchmarks of [10] and [42] remain. We add 11 additional benchmarks which have either been introduced in the literature on probabilistic programming [4,22,38], are adaptations of well-known stochastic processes or have been designed specifically to test unique features of AMBER. Notably, out of the 50 original benchmarks from [42] and [10], only 2 remain which are included in our benchmarks and which AMBER cannot prove PAST (because they are not Prob-solvable).…”

“…While [4] focused on computing statistical higher-order moments, our work addresses the termination behavior of probabilistic programs. The related approach of [22] computes exact expected runtimes of constant probability programs and provides a decision procedure for AST and PAST for such programs. Our programming model strictly generalizes the constant probability programs of [22], by supporting polynomial loop guards, updates and martingale expressions.…”

Automated Termination Analysis of Polynomial Probabilistic Programs

“…We present our experimental results by separating our benchmarks within three categories: (i) 21 programs which are PAST (Table 1), (ii) 11 programs which are AST (Table 2) but not necessarily PAST, and (iii) 6 programs which are not AST (Table 3). The benchmarks have either been introduced in the literature on probabilistic programming [40,9,4,21,37], are adaptations of well-known stochastic processes or have been designed specifically to test unique features of AMBER, like the ability to handle polynomial real arithmetic.…”

“…With these criteria, out of the 50 original benchmarks of [9] and [40] 10 remain. We augment these 10 programs with 11 additional benchmarks which have either been introduced in the literature on probabilistic programming [4,21,37], are adaptations of well-known stochastic processes or have been designed specifically to test unique features of AMBER. Notably, out of the 50 original benchmarks from [40] and [9], only 2 remain which are included in our benchmarks and which AMBER cannot prove PAST (because they are not Prob-solvable).…”