Syntax-Driven Private Evaluation of Quantified Membership Queries

2006 ◽  
pp. 470-485 ◽  
Author(s):  
Aggelos Kiayias ◽  
Antonina Mitrofanova
Keyword(s):  
Membership Queries

Attribute-efficient learning of Boolean functions from Post closed classes

2020 ◽  
Vol 30 (5) ◽  
pp. 285-301
Author(s):  
Anastasiya V. Bistrigova
Keyword(s):  
Boolean Functions ◽  
Membership Queries ◽  
Efficient Learning

AbstractWe consider exact attribute-efficient learning of functions from Post closed classes using membership queries and obtain bounds on learning complexity.

scholarly journals Compositional learning of mutually recursive procedural systems

2021 ◽  
Author(s):  
Markus Frohme ◽  
Bernhard Steffen
Keyword(s):  
Finite Automata ◽  
Simultaneous Inference ◽  
Recursive Structure ◽  
Recursive Models ◽  
Membership Queries ◽  
Compositional Approach ◽  
Recursive Programs ◽  
Automata Learning ◽  
The Individual ◽  
Compositional Learning

AbstractThis paper presents a compositional approach to active automata learning of Systems of Procedural Automata (SPAs), an extension of Deterministic Finite Automata (DFAs) to systems of DFAs that can mutually call each other. SPAs are of high practical relevance, as they allow one to efficiently learn intuitive recursive models of recursive programs after an easy instrumentation that makes calls and returns observable. Key to our approach is the simultaneous inference of individual DFAs for each of the involved procedures via expansion and projection: membership queries for the individual DFAs are expanded to membership queries of the entire SPA, and global counterexample traces are transformed into counterexamples for the DFAs of concerned procedures. This reduces the inference of SPAs to a simultaneous inference of the DFAs for the involved procedures for which we can utilize various existing regular learning algorithms. The inferred models are easy to understand and allow for an intuitive display of the procedural system under learning that reveals its recursive structure. We implemented the algorithm within the LearnLib framework in order to provide a ready-to-use tool for practical application which is publicly available on GitHub for experimentation.

DERANDOMIZED LEARNING OF BOOLEAN FUNCTIONS OVER FINITE ABELIAN GROUPS

2001 ◽  
Vol 12 (04) ◽  
pp. 491-516
Author(s):  
M. SITHARAM ◽  
TIMOTHY STRANEY
Keyword(s):  
Boolean Functions ◽  
Partial Information ◽  
Abelian Groups ◽  
Query Complexity ◽  
Character Theory ◽  
Finite Abelian Groups ◽  
Training Set ◽  
Membership Queries ◽  
Approximation Classes ◽  
Query Model

We employ the Always Approximately Correct or AAC model defined in [35], to prove learnability results for classes of Boolean functions over arbitrary finite Abelian groups. This model is an extension of Angluin's Query model of exact learning. The Boolean functions we consider belong to approximation classes, i.e. functions that are approximable (in various norms) by few Fourier basis functions, or irreducible characters of the domain Abelian group. We contrast our learnability results to previous results for similar classes in the PAC model of learning with and without membership queries. In addition, we discuss new, natural issues and questions that arise when the AAC model is used. One such question is whether a uniform training set is available for learning any function in a given approximation class. No analogous question seems to have been studied in the context of Angluin's Query model. Another question is whether the training set can be found quickly if the approximation class of the function is completely unknown to the learner, or only partial information about the approximation class is given to the learner (in addition to the answers to membership queries). In order to prove the learnability results in this paper we require new techniques for efficiently sampling Boolean functions using the character theory of finite Abelian groups, as well as the development of algebraic algorithms. The techniques result in other natural applications closely related to learning, for example, query complexity of deterministic algorithms for testing linearity, efficient pseudorandom generators, and estimating VC dimensions for classes of Boolean functions over finite Abelian groups.

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