On Separation Logic, Computational Independence, and Pseudorandomness (Extended Version)

• URL: http://arxiv.org/abs/2405.11987v1
• Date: Mon, 20 May 2024 12:39:28 GMT
• Title: On Separation Logic, Computational Independence, and Pseudorandomness (Extended Version)
• Authors: Ugo Dal Lago, Davide Davoli, Bruce M. Kapron,
• Abstract summary: This work explores the nature of computational independence in a cryptographic scenario. We show that the semantics of separation logic can be adapted so as to account for complexity bounded adversaries. Remarkably, this allows for a fruitful interplay between independence and pseudorandomness.
• Score: 1.024113475677323
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving semantics to separation logic formulas in which separating conjunction is interpreted in terms of probabilistic independence. The latter is taken in its exact form, i.e., two events are independent if and only if the joint probability is the product of the probabilities of the two events. There is indeed a literature on weaker notions of independence which are computational in nature, i.e. independence holds only against efficient adversaries and modulo a negligible probability of success. The aim of this work is to explore the nature of computational independence in a cryptographic scenario, in view of the aforementioned advances in separation logic. We show on the one hand that the semantics of separation logic can be adapted so as to account for complexity bounded adversaries, and on the other hand that the obtained logical system is useful for writing simple and compact proofs of standard cryptographic results in which the adversary remains hidden. Remarkably, this allows for a fruitful interplay between independence and pseudorandomness, itself a crucial notion in cryptography.

Related papers

• On the Independencies Hidden in the Structure of a Probabilistic Logic Program [0.0]
  We compute conditional independencies from d-separation in acyclic ground logic programs. We present a correct meta-interpreter that decides whether a certain conditional independence statement is implied by a program structure.
  arXiv  Detail & Related papers  (2023-08-30T08:55:55Z)
• Modeling Hierarchical Reasoning Chains by Linking Discourse Units and Key Phrases for Reading Comprehension [80.99865844249106]
  We propose a holistic graph network (HGN) which deals with context at both discourse level and word level, as the basis for logical reasoning. Specifically, node-level and type-level relations, which can be interpreted as bridges in the reasoning process, are modeled by a hierarchical interaction mechanism.
  arXiv  Detail & Related papers  (2023-06-21T07:34:27Z)
• An elementary belief function logic [6.091096843566857]
  duality between possibility and necessity measures, belief and plausibility functions and imprecise probabilities share a common feature with modal logic. This paper shows that a simpler belief function logic can be devised by adding Lukasiewicz logic on top of MEL.
  arXiv  Detail & Related papers  (2023-03-23T10:39:18Z)
• Logical Satisfiability of Counterfactuals for Faithful Explanations in NLI [60.142926537264714]
  We introduce the methodology of Faithfulness-through-Counterfactuals. It generates a counterfactual hypothesis based on the logical predicates expressed in the explanation. It then evaluates if the model's prediction on the counterfactual is consistent with that expressed logic.
  arXiv  Detail & Related papers  (2022-05-25T03:40:59Z)
• Adaptive n-ary Activation Functions for Probabilistic Boolean Logic [2.294014185517203]
  We show that we can learn arbitrary logic in a single layer using an activation function of matching or greater arity. We represent belief tables using a basis that directly associates the number of nonzero parameters to the effective arity of the belief function. This opens optimization approaches to reduce logical complexity by inducing parameter sparsity.
  arXiv  Detail & Related papers  (2022-03-16T22:47:53Z)
• Logical Credal Networks [87.25387518070411]
  This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. We investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud.
  arXiv  Detail & Related papers  (2021-09-25T00:00:47Z)
• Uncertain Linear Logic via Fibring of Probabilistic and Fuzzy Logic [0.0]
  probabilistic and fuzzy logic correspond to two different assumptions regarding the combination of propositions whose evidence bases are not currently available. It is shown that these two sets of formulas provide a natural grounding for the multiplicative and additive operator-sets in linear logic. The concept of linear logic as a logic of resources" is manifested here via the principle of conservation of evidence"
  arXiv  Detail & Related papers  (2020-09-28T00:19:42Z)
• Tractable Inference in Credal Sentential Decision Diagrams [116.6516175350871]
  Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. We develop the credal sentential decision diagrams, a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with credal sets of mass functions. For a first empirical validation, we consider a simple application based on noisy seven-segment display images.
  arXiv  Detail & Related papers  (2020-08-19T16:04:34Z)
• Foundations of Reasoning with Uncertainty via Real-valued Logics [70.43924776071616]
  We give a sound and strongly complete axiomatization that can be parametrized to cover essentially every real-valued logic. Our class of sentences are very rich, and each describes a set of possible real values for a collection of formulas of the real-valued logic.
  arXiv  Detail & Related papers  (2020-08-06T02:13:11Z)
• Logical Neural Networks [51.46602187496816]
  We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning) Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omni rather than focused on predefined target variables, and corresponds to logical reasoning.
  arXiv  Detail & Related papers  (2020-06-23T16:55:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.