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The number of steps until termination of a probabilistic program is a random variable. Probabilistic program termination therefore requires qualitative analysis via almost-sure termination (AST), while also providing quantitative answers…

Logic in Computer Science · Computer Science 2025-06-18 Lorenz Winkler , Laura Kovács

In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: 1. qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii)…

Logic in Computer Science · Computer Science 2015-10-30 Krishnendu Chatterjee , Hongfei Fu , Petr Novotny , Rouzbeh Hasheminezhad

Many programs allow the user to input data several times during its execution. If the program runs forever the user may input data infinitely often. A program terminates if it terminates no matter what the user does. We discuss various ways…

Combinatorics · Mathematics 2014-11-04 William Gasarch

We describe the Amber tool for proving and refuting the termination of a class of probabilistic while-programs with polynomial arithmetic, in a fully automated manner. Amber combines martingale theory with properties of asymptotic bounding…

Programming Languages · Computer Science 2021-07-29 Marcel Moosbrugger , Ezio Bartocci , Joost-Pieter Katoen , Laura Kovács

We consider imperative programs that involve both randomization and pure nondeterminism. The central question is how to find a strategy resolving the pure nondeterminism such that the so-obtained determinized program satisfies a given…

Logic in Computer Science · Computer Science 2023-11-15 Kevin Batz , Tom Jannik Biskup , Joost-Pieter Katoen , Tobias Winkler

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…

Programming Languages · Computer Science 2018-11-16 Toru Takisaka , Yuichiro Oyabu , Natsuki Urabe , Ichiro Hasuo

There are many evaluation strategies for term rewrite systems, but proving termination automatically is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies full termination. We adapt…

Logic in Computer Science · Computer Science 2024-02-13 Jan-Christoph Kassing , Florian Frohn , Jürgen Giesl

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…

Symbolic Computation · Computer Science 2018-02-28 Martin Avanzini , Ugo Dal Lago , Akihisa Yamada

We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…

Quantum Physics · Physics 2016-10-27 J. Calsamiglia , B. Gendra , R. Munoz-Tapia , E. Bagan

We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all…

Logic in Computer Science · Computer Science 2025-07-02 Éléanore Meyer , Jürgen Giesl

Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…

History and Overview · Mathematics 2007-05-23 Germano D'Abramo

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…

Programming Languages · Computer Science 2017-01-17 Ugo Dal Lago , Charles Grellois

Probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating…

Programming Languages · Computer Science 2021-01-25 Jules Jacobs

We study the almost sure convergence of randomly truncated stochastic algorithms. We present a new convergence theorem which extends the already known results by making vanish the classical condition on the noise terms. The aim of this work…

Probability · Mathematics 2009-06-29 Jérôme Lelong

We show that a subclass of infinite-state probabilistic programs that can be modeled by probabilistic one-counter automata (pOC) admits an efficient quantitative analysis. In particular, we show that the expected termination time can be…

Formal Languages and Automata Theory · Computer Science 2011-02-15 Tomas Brazdil , Stefan Kiefer , Antonin Kucera

We consider nondeterministic probabilistic programs with the most basic liveness property of termination. We present efficient methods for termination analysis of nondeterministic probabilistic programs with polynomial guards and…

Programming Languages · Computer Science 2016-04-26 Krishnendu Chatterjee , Hongfei Fu , Amir Kafshdar Goharshady

Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…

Information Theory · Computer Science 2007-07-13 Cristian S. Calude , Michael A. Stay

A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…

Optimization and Control · Mathematics 2023-11-21 Xun Shen , Satoshi Ito

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…

Logic in Computer Science · Computer Science 2024-11-12 Simon Oddershede Gregersen , Alejandro Aguirre , Philipp G. Haselwarter , Joseph Tassarotti , Lars Birkedal

The problem of determining whether or not any program terminates was shown to be undecidable by Turing, but recent advances in the area have allowed this information to be determined for a large class of programs. The classic method for…

Logic in Computer Science · Computer Science 2020-08-10 G. W. Hamilton