Tail-Bound Cost Analysis over Nondeterministic Probabilistic Programs

For probabilistic programs, there is some work for qualitative and quantitative analysis about expectation or mean, such as expected termination time, and expected cost analysis. However, another non-trivial issue is about tail bounds (i.e., upper bounds of tail probabilities), which can provide hig...

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Bibliographic Details
Published in:Shanghai jiao tong da xue xue bao Vol. 28; no. 6; pp. 772 - 782
Main Author: Wang, Peixin
Format: Journal Article
Language:English
Published: Shanghai Shanghai Jiaotong University Press 01.12.2023
Springer Nature B.V
Subjects:
Algorithms
Architecture
Computer Science
Cost analysis
Electrical Engineering
Engineering
Life Sciences
Materials Science
Polynomials
Qualitative analysis
Statistical analysis
Tails
Upper bounds
program cost analysis
A
尾部界限
probabilistic programs
鞅
TP 31
martingales
tail bound
程序消耗分析
概率程序
ISSN:1007-1172, 1674-8115, 1995-8188
Online Access:Get full text
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Summary:For probabilistic programs, there is some work for qualitative and quantitative analysis about expectation or mean, such as expected termination time, and expected cost analysis. However, another non-trivial issue is about tail bounds (i.e., upper bounds of tail probabilities), which can provide high-probability guarantees to extreme events. In this work, we focus on the problem of tail-bound cost analysis over nondeterministic probabilistic programs, which aims to automatically obtain the tail bound of resource usages over such programs. To achieve this goal, we present a novel approach, combined with a suitable concentration inequality, to derive the tail bound of accumulated cost until program termination. Our approach can handle both positive and negative costs. Moreover, our approach enables an automated template-based synthesis of supermartingales and leads to an efficient polynomial-time algorithm. To show the effectiveness of our approach, we present experimental results on various programs and make a comparison with state-of-the-art tools.
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ISSN:1007-1172
1674-8115
1995-8188
DOI:10.1007/s12204-022-2456-z