A Demonic Outcome Logic for Randomized Nondeterminism
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909396888453120 |
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| author | Zilberstein, Noam Kozen, Dexter Silva, Alexandra Tassarotti, Joseph |
| author_facet | Zilberstein, Noam Kozen, Dexter Silva, Alexandra Tassarotti, Joseph |
| contents | Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for concurrency, efficiency, or algorithmic design). In this paper, we introduce Demonic Outcome Logic for reasoning about programs that exploit both randomization and nondeterminism. The logic includes several novel features, such as reasoning about multiple executions in tandem and manipulating pre- and postconditions using familiar equational laws -- including the distributive law of probabilistic choices over nondeterministic ones. We also give rules for loops that both establish termination and quantify the distribution of final outcomes from a single premise. We illustrate the reasoning capabilities of Demonic Outcome Logic through several case studies, including the Monty Hall problem, an adversarial protocol for simulating fair coins, and a heuristic based probabilistic SAT solver. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Demonic Outcome Logic for Randomized Nondeterminism Zilberstein, Noam Kozen, Dexter Silva, Alexandra Tassarotti, Joseph Logic in Computer Science Programming Languages Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for concurrency, efficiency, or algorithmic design). In this paper, we introduce Demonic Outcome Logic for reasoning about programs that exploit both randomization and nondeterminism. The logic includes several novel features, such as reasoning about multiple executions in tandem and manipulating pre- and postconditions using familiar equational laws -- including the distributive law of probabilistic choices over nondeterministic ones. We also give rules for loops that both establish termination and quantify the distribution of final outcomes from a single premise. We illustrate the reasoning capabilities of Demonic Outcome Logic through several case studies, including the Monty Hall problem, an adversarial protocol for simulating fair coins, and a heuristic based probabilistic SAT solver. |
| title | A Demonic Outcome Logic for Randomized Nondeterminism |
| topic | Logic in Computer Science Programming Languages |
| url | https://arxiv.org/abs/2410.22540 |