Author

# Saurabh Srivastava

Other affiliations: University of California, Berkeley, Microsoft, Indian Institute of Technology Kanpur ...read more

Bio: Saurabh Srivastava is an academic researcher from Indian Institutes of Technology. The author has contributed to research in topic(s): Program synthesis & Predicate abstraction. The author has an hindex of 15, co-authored 52 publication(s) receiving 1258 citation(s). Previous affiliations of Saurabh Srivastava include University of California, Berkeley & Microsoft.

##### Papers published on a yearly basis

##### Papers

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TL;DR: The proposed technique synthesizes programs for complicated arithmetic algorithms including Strassen's matrix multiplication and Bresenham's line drawing; several sorting algorithms; and several dynamic programming algorithms using verification tools built in the VS3 project.

Abstract: This paper describes a novel technique for the synthesis of imperative programs. Automated program synthesis has the potential to make programming and the design of systems easier by allowing programs to be specified at a higher-level than executable code. In our approach, which we call proof-theoretic synthesis, the user provides an input-output functional specification, a description of the atomic operations in the programming language, and a specification of the synthesized program's looping structure, allowed stack space, and bound on usage of certain operations. Our technique synthesizes a program, if there exists one, that meets the input-output specification and uses only the given resources.The insight behind our approach is to interpret program synthesis as generalized program verification, which allows us to bring verification tools and techniques to program synthesis. Our synthesis algorithm works by creating a program with unknown statements, guards, inductive invariants, and ranking functions. It then generates constraints that relate the unknowns and enforces three kinds of requirements: partial correctness, loop termination, and well-formedness conditions on program guards. We formalize the requirements that program verification tools must meet to solve these constraint and use tools from prior work as our synthesizers.We demonstrate the feasibility of the proposed approach by synthesizing programs in three different domains: arithmetic, sorting, and dynamic programming. Using verification tools that we previously built in the VS3 project we are able to synthesize programs for complicated arithmetic algorithms including Strassen's matrix multiplication and Bresenham's line drawing; several sorting algorithms; and several dynamic programming algorithms. For these programs, the median time for synthesis is 14 seconds, and the ratio of synthesis to verification time ranges between 1x to 92x (with an median of 7x), illustrating the potential of the approach.

302 citations

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TL;DR: This paper shows how the constraint- based approach can be used to model a wide spectrum of program analyses in an expressive domain containing disjunctions and conjunctions of linear inequalities, and presents the first constraint-based approach to weakest precondition and strongest postcondition inference.

Abstract: A constraint-based approach to invariant generation in programs translates a program into constraints that are solved using off-the-shelf constraint solvers to yield desired program invariants.In this paper we show how the constraint-based approach can be used to model a wide spectrum of program analyses in an expressive domain containing disjunctions and conjunctions of linear inequalities. In particular, we show how to model the problem of context-sensitive interprocedural program verification. We also present the first constraint-based approach to weakest precondition and strongest postcondition inference. The constraints we generate are boolean combinations of quadratic inequalities over integer variables. We reduce these constraints to SAT formulae using bitvector modeling and use off-the-shelf SAT solvers to solve them.Furthermore, we present interesting applications of the above analyses, namely bounds analysis and generation of most-general counter-examples for both safety and termination properties. We also present encouraging preliminary experimental results demonstrating the feasibility of our technique on a variety of challenging examples.

227 citations

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TL;DR: Three novel algorithms are presented, having different strengths, that combine template and predicate abstraction based formalisms to discover required sophisticated program invariants using SMT solvers, and can verify program properties that, to the knowledge, have not been automatically verified before.

Abstract: We address the problem of automatically generating invariants with quantified and boolean structure for proving the validity of given assertions or generating pre-conditions under which the assertions are valid. We present three novel algorithms, having different strengths, that combine template and predicate abstraction based formalisms to discover required sophisticated program invariants using SMT solvers.Two of these algorithms use an iterative approach to compute fixed-points (one computes a least fixed-point and the other computes a greatest fixed-point), while the third algorithm uses a constraint based approach to encode the fixed-point. The key idea in all these algorithms is to reduce the problem of invariant discovery to that of finding optimal solutions for unknowns (over conjunctions of some predicates from a given set) in a template formula such that the formula is valid.Preliminary experiments using our implementation of these algorithms show encouraging results over a benchmark of small but complicated programs. Our algorithms can verify program properties that, to our knowledge, have not been automatically verified before. In particular, our algorithms can generate full correctness proofs for sorting algorithms (which requires nested universally-existentially quantified invariants) and can also generate preconditions required to establish worst-case upper bounds of sorting algorithms. Furthermore, for the case of previously considered properties, in particular sortedness in sorting algorithms, our algorithms take less time than reported by previous techniques.

134 citations

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TL;DR: This work shows how to reduce the template-based search problem to satisfiability solving, which permits the use of off-the-shelf solvers to efficiently explore the search space.

Abstract: Program verification is the task of automatically generating proofs for a program’s compliance with a given specification. Program synthesis is the task of automatically generating a program that meets a given specification. Both program verification and program synthesis can be viewed as search problems, for proofs and programs, respectively. For these search problems, we present approaches based on user-provided insights in the form of templates. Templates are hints about the syntactic forms of the invariants and programs, and help guide the search for solutions. We show how to reduce the template-based search problem to satisfiability solving, which permits the use of off-the-shelf solvers to efficiently explore the search space. Template-based approaches have allowed us to verify and synthesize programs outside the abilities of previous verifiers and synthesizers. Our approach can verify and synthesize difficult algorithmic textbook programs (e.g., sorting and dynamic programming-based algorithms) and difficult arithmetic programs.

71 citations

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04 Jun 2011

TL;DR: The problem of semi-automated inversion of imperative programs, which has the potential to make it much easier and less error prone to write programs that naturally pair as inverses, is investigated and a novel synthesis technique called Path-based inductive synthesis (PINS) is proposed.

Abstract: In this paper, we investigate the problem of semi-automated inversion of imperative programs, which has the potential to make it much easier and less error prone to write programs that naturally pair as inverses, such as insert/delete operations, compressors/decompressors, and so on. Viewing inversion as a subproblem of program synthesis, we propose a novel synthesis technique called Path-based inductive synthesis (PINS) and apply it to inversion. PINS starts from a program P and a template T for its inverse. PINS then iteratively refines the space of template instantiations by exploring paths in the composition of P and T with symbolic execution. PINS uses an SMT solver to intelligently guide the refinement process, based on the paths explored so far. The key idea motivating this approach is the small path-bound hypothesis: that the behavior of a program can be summarized with a small, carefully chosen set of its program paths.We evaluated PINS by using it to invert 14 programs such as compressors (e.g., Lempel-Ziv-Welch), encoders (e.g., UUEncode), and arithmetic operations (e.g., vector rotation). Most of these examples are difficult or impossible to invert using prior techniques, but PINS was able to invert all of them. We also found that a semi-automated technique we developed to mine a template from the program to be inverted worked well. In our experiments, PINS takes between one second to thirty minutes to synthesize inverses. We believe this proof-of-concept implementation demonstrates the viability of the PINS approach to program synthesis.

65 citations

##### Cited by

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AT&T

^{1}TL;DR: This ebook is the first authorized digital version of Kernighan and Ritchie's 1988 classic, The C Programming Language (2nd Ed.), and is a "must-have" reference for every serious programmer's digital library.

Abstract: This ebook is the first authorized digital version of Kernighan and Ritchie's 1988 classic, The C Programming Language (2nd Ed.). One of the best-selling programming books published in the last fifty years, "K&R" has been called everything from the "bible" to "a landmark in computer science" and it has influenced generations of programmers. Available now for all leading ebook platforms, this concise and beautifully written text is a "must-have" reference for every serious programmers digital library.
As modestly described by the authors in the Preface to the First Edition, this "is not an introductory programming manual; it assumes some familiarity with basic programming concepts like variables, assignment statements, loops, and functions. Nonetheless, a novice programmer should be able to read along and pick up the language, although access to a more knowledgeable colleague will help."

2,120 citations

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01 Jan 2009

TL;DR: This paper presents a meta-modelling framework for modeling and testing the robustness of the modeled systems and some of the techniques used in this framework have been developed and tested in the field.

Abstract: ing WS1S Systems to Verify Parameterized Networks . . . . . . . . . . . . 188 Kai Baukus, Saddek Bensalem, Yassine Lakhnech and Karsten Stahl FMona: A Tool for Expressing Validation Techniques over Infinite State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 J.-P. Bodeveix and M. Filali Transitive Closures of Regular Relations for Verifying Infinite-State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Bengt Jonsson and Marcus Nilsson Diagnostic and Test Generation Using Static Analysis to Improve Automatic Test Generation . . . . . . . . . . . . . 235 Marius Bozga, Jean-Claude Fernandez and Lucian Ghirvu Efficient Diagnostic Generation for Boolean Equation Systems . . . . . . . . . . . . 251 Radu Mateescu Efficient Model-Checking Compositional State Space Generation with Partial Order Reductions for Asynchronous Communicating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 Jean-Pierre Krimm and Laurent Mounier Checking for CFFD-Preorder with Tester Processes . . . . . . . . . . . . . . . . . . . . . . . 283 Juhana Helovuo and Antti Valmari Fair Bisimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Thomas A. Henzinger and Sriram K. Rajamani Integrating Low Level Symmetries into Reachability Analysis . . . . . . . . . . . . . 315 Karsten Schmidt Model-Checking Tools Model Checking Support for the ASM High-Level Language . . . . . . . . . . . . . . 331 Giuseppe Del Castillo and Kirsten Winter Table of

1,687 citations

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01 Jan 1997

TL;DR: In this article, the spectral ratio between horizontal and vertical components (H/V ratio) of microtremors measured at the ground surface has been used to estimate fundamental periods and amplification factors of a site, although this technique lacks theoretical background.

Abstract:
The spectral ratio between horizontal and vertical components (H/V ratio) of microtremors measured at the ground surface has been used to estimate fundamental periods and amplification factors of a site, although this technique lacks theoretical background. The aim of this article is to formulate the H/V technique in terms of the characteristics of Rayleigh and Love waves, and to contribute to improve the technique. The improvement includes use of not only peaks but also troughs in the H/V ratio for reliable estimation of the period and use of a newly proposed smoothing function for better estimation of the amplification factor. The formulation leads to a simple formula for the amplification factor expressed with the H/V ratio. With microtremor data measured at 546 junior high schools in 23 wards of Tokyo, the improved technique is applied to mapping site periods and amplification factors in the area.

984 citations

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Microsoft

^{1}TL;DR: The design of a string programming/expression language that supports restricted forms of regular expressions, conditionals and loops is described and an algorithm based on several novel concepts for synthesizing a desired program in this language is described from input-output examples.

Abstract: We describe the design of a string programming/expression language that supports restricted forms of regular expressions, conditionals and loops. The language is expressive enough to represent a wide variety of string manipulation tasks that end-users struggle with. We describe an algorithm based on several novel concepts for synthesizing a desired program in this language from input-output examples. The synthesis algorithm is very efficient taking a fraction of a second for various benchmark examples. The synthesis algorithm is interactive and has several desirable features: it can rank multiple solutions and has fast convergence, it can detect noise in the user input, and it supports an active interaction model wherein the user is prompted to provide outputs on inputs that may have multiple computational interpretations.The algorithm has been implemented as an interactive add-in for Microsoft Excel spreadsheet system. The prototype tool has met the golden test - it has synthesized part of itself, and has been used to solve problems beyond author's imagination.

663 citations

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TL;DR: The main idea is to reduce the problem of code completion to a natural-language processing problem of predicting probabilities of sentences, and design a simple and scalable static analysis that extracts sequences of method calls from a large codebase, and index these into a statistical language model.

Abstract: We address the problem of synthesizing code completions for programs using APIs. Given a program with holes, we synthesize completions for holes with the most likely sequences of method calls. Our main idea is to reduce the problem of code completion to a natural-language processing problem of predicting probabilities of sentences. We design a simple and scalable static analysis that extracts sequences of method calls from a large codebase, and index these into a statistical language model. We then employ the language model to find the highest ranked sentences, and use them to synthesize a code completion. Our approach is able to synthesize sequences of calls across multiple objects together with their arguments. Experiments show that our approach is fast and effective. Virtually all computed completions typecheck, and the desired completion appears in the top 3 results in 90% of the cases.

491 citations