Justin Hsu’s research while affiliated with Cornell University and other places

... [11,13]). New equivalences keep appearing in the literature, such as the recently introduced convex language semantics of nondeterministic probabilistic automata [37]. ...

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Graded Monads for the Linear Time - Branching Time Spectrum

... It remains unclear whether probability independence is provable by bisimulation when the output distribution is non-uniform. Symbolic inference [92]- [94] provides automated methods to answer symbolic queries about distributions induced by probabilistic programs. Though it is possible to encode uniformity queries in such methods, existing formalisms of symbolic inference [44] fall short in specifying parameterized systems like those considered by this work. ...

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Probabilistic Bisimulation for Parameterized Anonymity and Uniformity Verification

... The weakest pre-expectation transformer [McIver and Morgan 2005;Olmedo et al. 2016] is a generalisation of the weakest precondition transformer [Dijkstra 1975]. This notion is used to verify properties such as termination probabilities and probabilistic invariants [Bao et al. 2022;Batz et al. 2023] for imperative probabilistic programming languages. The expected runtime transformer ] is a similar notion proposed for verification of expected costs. ...

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Automated Verification of Higher-Order Probabilistic Programs via a Dependent Refinement Type System

... Originally [46], the resources were data structures in memory, and the separating conjunction guaranteed the absence of aliasing. In modern versions of the logic, this has been generalized to cover other types of resources, such as the state of a concurrent protocol [29] or sources of randomness [9,7,37]. ...

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Cryptis: Cryptographic Reasoning in Separation Logic

... While the mathematical semantics of such programs is fairly well-understood [1], verification methods remain an active area of research. Existing automated techniques are either limited to specific properties (e.g., [2][3][4][5]), or target simpler computational models [6][7][8]. ...

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Data-driven invariant learning for probabilistic programs

... Capturing probabilistic independence in separation logic was first explored by Barthe et al. [2019], however the resulting Probabilistic Separation Logic (PSL) was limited in its ability to reason about control flow, and the frame rule had stringent side conditions. DIBI later extended the PSL model to include conditioning, but did not include a full program logic [Bao et al. 2021]. Lilac built on the two aforementioned logics and used conditioning to improve on PSL's handling of control flow, although without mutable state [Li et al. 2023]. ...

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Probabilistic Concurrent Reasoning in Outcome Logic: Independence, Conditioning, and Invariants

... These encoding are well-known in propositional dynamic logic [22,16] and Kleene algebra with tests (KAT) [23,24]. The set of PWP terms is the minimal subset W of PCoR { * } satisfying the following: ...

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Undecidability of the Emptiness Problem of Deterministic Propositional While Programs with Graph Loop: Hypothesis Elimination Using Loops

... The goal is to query for various properties about the network's behavior: for instance, the probability of a packet reaching the end of the network, or of a packet queue overflowing. This example task is inspired by prior work on using probabilistic programming languages to perform network verification [18,53]. The situation in Fig. 1 is a small illustrative example of packet arrival, but programs like it are extremely challenging for today's PPLs because they mix different kinds of program structure. ...

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Multi-Language Probabilistic Programming

... There are also many domain-specific automated analyses for specific probabilistic properties, such as termination and resource analysis [Chatterjee et al. 2016;Moosbrugger et al. 2021;Wang et al. 2021], accuracy Smith et al. 2019], reliability [Carbin et al. 2012], differential privacy [Albarghouthi and Hsu 2018b;Barthe et al. 2021] and other relational properties [Albarghouthi and Hsu 2018a;Farina et al. 2021], and long-run properties of probabilistic loops [Bartocci et al. 2019[Bartocci et al. , 2020. Our approach aims to create a general-purpose analysis. ...

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Symbolic Execution for Randomized Programs