Related papers: Modular Verification for Almost-Sure Termination o…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so; it…
We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover,…
The extension of classical imperative programs with real-valued random variables and random branching gives rise to probabilistic programs. The termination problem is one of the most fundamental liveness properties for such programs. The…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of…
We study the recursion-theoretic complexity of Positive Almost-Sure Termination ($\mathsf{PAST}$) in an imperative programming language with rational variables, bounded nondeterministic choice, and discrete probabilistic choice. A program…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates…
Extending our own and others' earlier approaches to reasoning about termination of probabilistic programs, we propose and prove a new rule for termination with probability one, also known as "almost-certain termination". The rule uses both…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
We study the termination problem for nondeterministic recursive probabilistic programs. First, we show that a ranking-supermartingales-based approach is both sound and complete for bounded terminiation (i.e., bounded expected termination…
The termination behavior of probabilistic programs depends on the outcomes of random assignments. Almost sure termination (AST) is concerned with the question whether a program terminates with probability one on all possible inputs.…
This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a…
We introduce a method for proving almost sure termination in the context of lambda calculus with continuous random sampling and explicit recursion, based on ranking supermartingales. This result is extended in three ways. Antitone ranking…
Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure)…
In recent years, numerous techniques were developed to automatically prove termination of different kinds of probabilistic programs. However, there are only few automated methods to disprove their termination. In this paper, we present the…
We introduce a system of monadic affine sized types, which substantially generalise usual sized types, and allows this way to capture probabilistic higher-order programs which terminate almost surely. Going beyond plain, strong…
Almost-sure termination is an important correctness property for probabilistic programs, and a number of program logics have been developed for establishing it. However, these logics have mostly been developed for first-order programs…
This paper presents a wp-style calculus for obtaining bounds on the expected run-time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination time of a probabilistic program and proving…