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On Lexicographic Proof Rules for Probabilistic Termination [article]

Krishnendu Chatterjee, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, Đorđe Žikelić
2021 arXiv   pre-print
This standard feature of non-probabilistic termination proofs was hitherto not known to be sound in the probabilistic setting, as the soundness proof requires a careful analysis of the underlying stochastic  ...  Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking  ...  /3385412.3386002, gorithms for the Construction and Analysis of Systems, 7th International Confer- ence, TACAS 2001 Held as Part of the Joint European Conferences on Theory and Practice of Software,  ... 
arXiv:2108.02188v1 fatcat:5xnql7jo6bcatbw2t3stsics5q

Automated Recurrence Analysis for Almost-Linear Expected-Runtime Bounds [article]

Krishnendu Chatterjee, Hongfei Fu, Aniket Murhekar
2017 arXiv   pre-print
We have implemented our approach, and the experimental results show that we obtain the bounds efficiently for the recurrences of various classical algorithms.  ...  Our main contribution is an efficient (simple linear-time algorithm) sound approach for deriving such expected-runtime bounds for the analysis of recurrence relations induced by randomized algorithms.  ...  Tools and Algorithms for the Construction and Analysis of Systems, 7th International Conference, TACAS 2001 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2001  ... 
arXiv:1705.00314v1 fatcat:77uvfirphfadlfrcttspsvc2fa

Automated Recurrence Analysis for Almost-Linear Expected-Runtime Bounds [chapter]

Krishnendu Chatterjee, Hongfei Fu, Aniket Murhekar
2017 Lecture Notes in Computer Science  
For the worst-case analysis there are several techniques, such as worst-case execution time analysis [47] , resource analysis using abstract interpretation and type systems [24, 2, 34, 26, 27] , ranking  ...  Our efficient (linear-time) algorithm can soundly infer logarithmic, linear, and almost-linear bounds for recurrences of one or two variables. 2. Analysis of classical algorithms.  ...  Tools and Algorithms for the Construction and Analysis of Systems, 7th International Conference, TACAS 2001 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2001  ... 
doi:10.1007/978-3-319-63387-9_6 fatcat:ofhiqtighrczbkxxnsowhqeffe

Non-polynomial Worst-Case Analysis of Recursive Programs [article]

Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady
2017 arXiv   pre-print
We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for  ...  the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where  ...  Tools and Algorithms for the Construction and Analysis of Systems, 7th International Conference, TACAS 2001 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2001  ... 
arXiv:1705.00317v1 fatcat:uprjjsi27razxcfqe4glhftzle

Non-polynomial Worst-Case Analysis of Recursive Programs [chapter]

Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady
2017 Lecture Notes in Computer Science  
For example, our approach cannot handle the Euclidean algorithm for computing the greatest common divisor of two given natural numbers, since the worstcase behaviour of this algorithm relies on Lamé's  ...  Moreover, as our computational tool is linear programming, the approach we provide is also a relatively scalable one (see Remark 5).  ...  Tools and Algorithms for the Construction and Analysis of Systems, 7th International Conference, TACAS 2001 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2001  ... 
doi:10.1007/978-3-319-63390-9_3 fatcat:k7stgjvdrzb5fglfev6dgwyh4q