Reasoning about programs in statistically modeled first-order environments

Mangal, Ravi

Title:

Reasoning about programs in statistically modeled first-order environments

dc.contributor.advisor	Orso, Alessandro
dc.contributor.author	Mangal, Ravi
dc.contributor.committeeMember	Sarkar, Vivek
dc.contributor.committeeMember	Zhang, Qirun
dc.contributor.committeeMember	Harris, William
dc.contributor.committeeMember	Nori, Aditya
dc.contributor.department	Computer Science
dc.date.accessioned	2021-01-11T17:09:43Z
dc.date.available	2021-01-11T17:09:43Z
dc.date.created	2020-12
dc.date.issued	2020-12-01
dc.date.submitted	December 2020
dc.date.updated	2021-01-11T17:09:43Z
dc.description.abstract	The objects of study in this dissertation are programs and algorithms that reason about programs using their syntactic structure. Such algorithms, referred to as program verification algorithms in the literature, are designed to find proofs of propositions about program behavior. This dissertation adopts the perspective that programs operate in environments that can be modeled statistically. In other words, program inputs are samples drawn from a generative statistical model. This statistical perspective has two main advantages. First, it allows us to reason about programs that are not expected to exhibit the desired behavior on all program inputs, such as neural networks that are learnt from data, by formulating and proving probabilistic propositions about program behavior. Second, it enables us to simplify the search for proofs of non-probabilistic propositions about program behavior by designing program verification algorithms that are capable of inferring “likely” hypotheses about the program environment. The first contribution of this dissertation is a pair of program verification algorithms for finding proofs of probabilistic robustness of neural networks. A trained neural network f is probabilistically robust if, for a pair of inputs that is randomly generated as per the environment statistical model, f is likely to demonstrate k-Lipschitzness, i.e., the distance between the outputs computed by f is upper-bounded by the kth multiple of the distance between the pair of inputs. A proof of probabilistic robustness guarantees that the neural network is unlikely to exhibit divergent behaviors on similar inputs. The second contribution of this dissertation is a generic algorithmic framework, referred to as observational abstract interpreters, for designing algorithms that compute hypothetical semantic program invariants. Semantic invariants are logical predicates about program behavior and are used in program proofs as lemmas. The well-studied algorithmic framework of abstract interpretation provides a standard recipe for constructing algorithms that compute semantic program invariants. Observational abstract interpreters extend this framework to allow for computing hypothetical invariants that are valid only under specific hypotheses about program environments. These hypotheses are inferred from observations of program behavior and are embedded as dynamic/run-time checks in the program to ensure the validity of program proofs that use hypothetical invariants.
dc.description.degree	Ph.D.
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1853/64117
dc.language.iso	en_US
dc.publisher	Georgia Institute of Technology
dc.subject	Program verification
dc.subject	Statistically modeled environments
dc.title	Reasoning about programs in statistically modeled first-order environments
dc.type	Text
dc.type.genre	Dissertation
dspace.entity.type	Publication
local.contributor.advisor	Orso, Alessandro
local.contributor.corporatename	College of Computing
local.contributor.corporatename	School of Computer Science
relation.isAdvisorOfPublication	d23047b9-62b9-40ea-a94a-2d6222c76191
relation.isOrgUnitOfPublication	c8892b3c-8db6-4b7b-a33a-1b67f7db2021
relation.isOrgUnitOfPublication	6b42174a-e0e1-40e3-a581-47bed0470a1e
thesis.degree.level	Doctoral