DOCSLIB.ORG

Faster and Better Simple Temporal Problems

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Faster and Better Simple Temporal Problems PRELIMINARY VERSION: DO NOT CITE The AAAI Digital Library will contain the published version some time after the conference Faster and Better Simple Temporal Problems Dario Ostuni1, Alice Raffaele2, Romeo Rizzi1, Matteo Zavatteri1* 1University of Verona, Department of Computer Science, Strada Le Grazie 15, 37134 Verona (Italy) 2University of Trento, Department of Mathematics, Via Sommarive 14, 38123 Povo (Italy) fdario.ostuni, romeo.rizzi, [email protected], [email protected] Abstract satisfied? TCSP is NP-complete (Dechter, Meiri, and Pearl 1991). In this paper we give a structural characterization and ex- tend the tractability frontier of the Simple Temporal Problem The Simple Temporal Problem (STP) is the fragment of (STP) by defining the class of the Extended Simple Temporal TCSP whose set of constraints consists of atoms of the form Problem (ESTP), which augments STP with strict inequal- y − x 2 [`; u] only. Historically, STP allows for two rep- ities and monotone Boolean formulae on inequations (i.e., resentations: the interval based one (as we just discussed formulae involving the operations of conjunction, disjunction above) or a set of inequalities y − x ≤ k where x; y are and parenthesization). A polynomial-time algorithm is pro- variables and k 2 R. While these are equivalent (y − x ≤ k vided to solve ESTP, faster than previous state-of-the-art al- can be written as y − x 2 [−∞; k]), the second represen- gorithms for other extensions of STP that had been consid- tation is more elementary as y − x 2 [`; u] amounts to ered in the literature, all encompassed by ESTP. We show the (y − x ≤ u) ^ (x − y ≤ −`). STP is in P (Dechter, Meiri, practical competitiveness of our approach through a proof-of- concept implementation and an experimental evaluation in- and Pearl 1991). volving also state-of-the-art SMT solvers. The set of constraints of an STP can also be generalized to include strict inequalities y − x < k and inequations y − x 6= k. Of course, any strict inequality y − x < k can be Introduction and Related Work seen as a non-strict inequality y − x ≤ k plus the inequation The Temporal Constraint Satisfaction Problem (TCSP), y − x 6= k. Inequations are useful to model temporal plans originally introduced by (Dechter, Meiri, and Pearl 1991), in which, for example, we require two events not to happen takes as input a finite set of real variables and a finite set at the same time. Koubarakis augmented STP with disjunc- of constraints. Two kinds of constraints are allowed: unary tions on inequations (y1 − x1 6= k1) _···_ (yn − xn 6= kn) and binary; both can take a disjunctive form. A unary con- in (Koubarakis 1992). He proved tractability of this exten- 4 straint has the form x 2 [`1; u1] _···_ [`n; un], where sion by providing an algorithm that runs in O(jjCjj ), where x is a variable and `i; ui 2 R [ {−∞; +1g, −∞ ≤ C is the set of constraints and jjCjj is the number of atoms `i ≤ ui ≤ 1. A binary constraint has the form y − x 2 y − x ./ k, ./2 {≤; 6=g appearing in C. As far as we know, [`1; u1] _···_ [`n; un], where x and y are variables and, this was still the bound for this problem. 6= again, `i; ui 2 R [ {−∞; +1g, −∞ ≤ `i ≤ ui ≤ 1. Gerevini and Cristani defined STP , which is a restric- Regardless of the type of constraint, the corresponding in- tion of (Koubarakis 1992) allowing only simple inequa- volved intervals are disjoint. Note that each unary constraint tions and not disjunctions of these, resulting in the possi- x 2 [`1; u1] _···_ [`n; un] can be seen as a binary one bility of handling both sets of strict-inequalities and inequa- x − z 2 [`1; u1] _···_ [`n; un] where z is an extra variable tions (Gerevini and Cristani 1997). They provided an algo- on which we impose the unary constraint z 2 [0; 0]. As such, rithm to solve STP6= that runs in O(n3 + h), where n is the one single unary constraint suffices. Or, we can even relax number of variables and h is the number of inequations (or that one and then consider the solution obtained by sub- O(n3) if there are only strict and non-strict inequalities). As tracting the value of z from that of every other variable. In- far as we know, the result in (Gerevini and Cristani 1997) deed, the solution space of a TCSP without unary constraints was the state of the art for STP6=, still used by more recent is closed under rigid shifting. We remark that binary con- works (e.g., (Broxvall 2002; Montanari et al. 2012; Cooper, straints are disjunctions over the same pair of variables (this Maris, and Regnier´ 2013; Carbonnel and Cooper 2015)). restriction is overcome in (Stergiou and Koubarakis 2000) For more details about temporal reasoning, the interested with the proposal of disjunctive temporal networks). TCSP reader is referred to (Vila 1994; Gennari 1998; Schwalb and asks the following question: does there exist an assignment Vila 1998; Bartak, Morris, and Venable 2014). of real values to the variables such that all constraints are Satisfiability Modulo Theory (SMT) (Barrett et al. 2009) *Corresponding author can address generalizations of the problems mentioned Copyright © 2021, Association for the Advancement of Artificial above by relying on the quantifier-free fragment of the the- Intelligence (www.aaai.org). All rights reserved. ory of real difference logic (QF RDL). QF RDL allows for arbitrary Boolean combinations of atoms y − x ./ k, where Example 1. Let S = (X; C) be the following instance of x; y are real variables and ./2 f<; ≤; >; ≥; =; 6=g. STP: X := fx1; x2; x3; x4; x5; x6; x7g, In this logic, strict inequalities y − x < k are usually turned into non-strict inequalities y − x ≤ k − ", with " C := fx2 − x1 ≤ −2:2; x3 − x2 ≤ −3:5; x1 − x3 ≤ 5:7; treated either numerically (Armando et al. 2005) or symbol- x4 − x5 ≤ 2; x5 − x7 ≤ 1; x7 − x6 ≤ 6; ically as an infinitesimal parameter (Dutertre and de Moura x6 − x4 ≤ −9; x6 − x3 ≤ −3:3; x2 − x4 ≤ −2g: 2006). As far as we know, the latter is the state of the art on difference arithmetic constraints (Dutertre and de Moura Most of the algorithms that solve instances of STP rely on 2006; de Moura, Dutertre, and Shankar 2007). their corresponding directed weighted graph representation. Note that the core algorithms to solve the problems men- Definition 1 (Directed weighted graph). A directed graph tioned above are typically based on tuned versions of short- is a pair (V; A) where V is a set of nodes and A ⊆ V × V est path algorithms or the simplex method, e.g., (SRI Inter- is a set of arcs (or, equivalently, directed edges). A directed national’s Computer Science Laboratory 2020). It is thus in- weighted graph is a triple (V; A; w) where (V; A) is a di- teresting and reasonable, e.g., when developing a more effi- rected graph and w : A 7! R is a weight function assigning cient procedure to solve STP with strict inequalities, to also a real value to each arc. make a comparison with SMT solvers supporting QF RDL. We write Px;y := h(x; x1);:::; (xn; y)i for the path (se- Organization and Contribution quence of arcs) going from x to y through a sequence of dis- tinct nodes. A cycle is a path P where x = y. In case of We start by giving background on STP. Then, we define x;y directed weighted graphs, we write w(P ) for the weight the Extended Simple Temporal Problem (ESTP), in which x;y of the path (i.e., the sum of the weights of the arcs in the we allow for inequalities, strict inequalities and monotone sequence). A path or a cycle P in a weighted graph is Boolean formulae on inequations. We give a characteriza- x;y negative if w(P ) < 0. tion of ESTP. Specifically, we define verification criteria to x;y detect inconsistency or decide consistency of any instance Definition 2 (Constraint graph). Let S = (X; C) be an in- of ESTP. These allow us to provide a strong polynomial- stance of STP. The corresponding constraint graph of S is time algorithm to solve ESTP, which is faster than current the directed weighted graph GS = (X; A; w) where: state-of-the-art algorithms for previously studied extended • A := f(x; y) j y − x ≤ k 2 Cg, and classes of STP. We discuss a proof-of-concept implementa- • w(x; y) := k for each y − x ≤ k 2 C. tion by comparing several variants of shortest paths algo- rithms. Moreover, we encode our model as a QF RDL for- Figure 1 shows the constraint graph of Example 1. mula since it is well-known that the satisfiability of conjunc- Theorem 1 ((Dechter, Meiri, and Pearl 1991)). An instance tions of atoms y − x ./ k for ./2 {≤; <g is tractable. We of STP is consistent iff GS has no negative-weight cycle. evaluate our performance against the state-of-the-art SMT solvers that competed in the 15th International Satisfiabil- Deciding whether an instance of STP S = (X; C) is con- ity Modulo Theories Competition — SMT-COMP 2020 — sistent can be done by computing a potential function for for QF RDL (Model Validation Track and Single Query GS, i.e., a function π : X 7! R such that π(y) − π(x) ≤ Track), (SMT Steering Committee 2020). Computational re- w(x; y) for each (x; y) 2 A.
Load more

Recommended publications
  • Autogr: Automated Geo-Replication with Fast System Performance and Preserved Application Semantics
    AutoGR: Automated Geo-Replication with Fast System Performance and Preserved Application Semantics Jiawei Wang1, Cheng Li1,4, Kai Ma1, Jingze Huo1, Feng Yan2, Xinyu Feng3, Yinlong Xu1,4 1University of Science and Technology of China 2University of Nevada, Reno 3State Key Laboratory for Novel Software Technology, Nanjing University 4Anhui Province Key Laboratory of High Performance Computing [email protected],{chengli7,ylxu}@ustc.edu.cn,{ksqsf,jzfire}@mail.ustc.edu.cn,[email protected],[email protected] ABSTRACT static runtime Geo-replication is essential for providing low latency response AP AP and quality Internet services. However, designing fast and correct Analyzer Code App ( Rigi ) geo-replicated services is challenging due to the complex trade-off US EU US EU between performance and consistency semantics in optimizing the expensive cross-site coordination. State-of-the-art solutions rely Restrictions on programmers to derive sufficient application-specific invariants Cross-site Causally Consistent Schema Coordination and code specifications, which is both time-consuming and error- Database Service Geo-Replicated Store prone. In this paper, we propose an end-to-end geo-replication APP Servers deployment framework AutoGR (AUTOmated Geo-Replication) to free programmers from such label-intensive tasks. AutoGR en- Figure 1: An overview of the proposed end-to-end AutoGR ables the geo-replication features for non-replicated, serializable solution. AP, US, and EU stand for data centers in Singapore, applications in an automated way with optimized performance and Oregon, and Frankfurt, respectively. The runtime library is correct application semantics. Driven by a novel static analyzer Rigi, co-located with Server, omitted from the graph.
    [Show full text]
  • Functional SMT Solving: a New Interface for Programmers
    Functional SMT solving: A new interface for programmers A thesis submitted in Partial Fulfillment of the Requirements for the Degree of Master of Technology by Siddharth Agarwal to the DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY KANPUR June, 2012 v ABSTRACT Name of student: Siddharth Agarwal Roll no: Y7027429 Degree for which submitted: Master of Technology Department: Computer Science & Engineering Thesis title: Functional SMT solving: A new interface for programmers Name of Thesis Supervisor: Prof Amey Karkare Month and year of thesis submission: June, 2012 Satisfiability Modulo Theories (SMT) solvers are powerful tools that can quickly solve complex constraints involving booleans, integers, first-order logic predicates, lists, and other data types. They have a vast number of potential applications, from constraint solving to program analysis and verification. However, they are so complex to use that their power is inaccessible to all but experts in the field. We present an attempt to make using SMT solvers simpler by integrating the Z3 solver into a host language, Racket. Our system defines a programmer’s interface in Racket that makes it easy to harness the power of Z3 to discover solutions to logical constraints. The interface, although in Racket, retains the structure and brevity of the SMT-LIB format. We demonstrate this using a range of examples, from simple constraint solving to verifying recursive functions, all in a few lines of code. To my grandfather Acknowledgements This project would have never have even been started had it not been for my thesis advisor Dr Amey Karkare’s help and guidance. Right from the time we were looking for ideas to when we finally had a concrete proposal in hand, his support has been invaluable.
    [Show full text]
  • Approximations and Abstractions for Reasoning About Machine Arithmetic
    IT Licentiate theses 2016-010 Approximations and Abstractions for Reasoning about Machine Arithmetic ALEKSANDAR ZELJIC´ UPPSALA UNIVERSITY Department of Information Technology Approximations and Abstractions for Reasoning about Machine Arithmetic Aleksandar Zeljic´ [email protected] October 2016 Division of Computer Systems Department of Information Technology Uppsala University Box 337 SE-751 05 Uppsala Sweden http://www.it.uu.se/ Dissertation for the degree of Licentiate of Philosophy in Computer Science c Aleksandar Zeljic´ 2016 ISSN 1404-5117 Printed by the Department of Information Technology, Uppsala University, Sweden Abstract Safety-critical systems rely on various forms of machine arithmetic to perform their tasks: integer arithmetic, fixed-point arithmetic or floating-point arithmetic. Machine arithmetic can exhibit subtle dif- ferences in behavior compared to the ideal mathematical arithmetic, due to fixed-size of representation in memory. Failure of safety-critical systems is unacceptable, because it can cost lives or huge amounts of money, time and e↵ort. To prevent such incidents, we want to form- ally prove that systems satisfy certain safety properties, or otherwise discover cases when the properties are violated. However, for this we need to be able to formally reason about machine arithmetic. The main problem with existing approaches is their inability to scale well with the increasing complexity of systems and their properties. In this thesis, we explore two alternatives to bit-blasting, the core procedure lying behind many common approaches to reasoning about machine arithmetic. In the first approach, we present a general approximation framework which we apply to solve constraints over floating-point arithmetic. It is built on top of an existing decision procedure, e.g., bit-blasting.
    [Show full text]
  • Automated Theorem Proving
    CS 520 Theory and Practice of Software Engineering Spring 2021 Automated theorem proving April 22, 2020 Upcoming assignments • Week 12 Par4cipaon Ques4onnaire will be about Automated Theorem Proving • Final project deliverables are due Tuesday May 11, 11:59 PM (just before midnight) Programs are known to be error-prone • Capture complex aspects such as: • Threads and synchronizaon (e.g., Java locks) • Dynamically heap allocated structured data types (e.g., Java classes) • Dynamically stack allocated procedures (e.g., Java methods) • Non-determinism (e.g., Java HashSet) • Many input/output pairs • Challenging to reason about all possible behaviors of these programs Programs are known to be error-prone • Capture complex aspects such as: • Threads and synchronizaon (e.g., Java locks) • Dynamically heap allocated structured data types (e.g., Java classes) • Dynamically stack allocated procedures (e.g., Java methods) • Non-determinism (e.g., Java HashSet) • Many input/output pairs • Challenging to reason about all possible behaviors of these programs Overview of theorem provers Key idea: Constraint sa4sfac4on problem Take as input: • a program modeled in first-order logic (i.e. a set of boolean formulae) • a queson about that program also modeled in first-order logic (i.e. addi4onal boolean formulae) Overview of theorem provers Use formal reasoning (e.g., decision procedures) to produce as output one of the following: • sasfiable: For some input/output pairs (i.e. variable assignments), the program does sasfy the queson • unsasfiable: For all
    [Show full text]
  • Learning-Aided Program Synthesis and Verification
    LEARNING-AIDED PROGRAM SYNTHESIS AND VERIFICATION Xujie Si A DISSERTATION in Computer and Information Science Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2020 Supervisor of Dissertation Mayur Naik, Professor, Computer and Information Science Graduate Group Chairperson Mayur Naik, Professor, Computer and Information Science Dissertation Committee: Rajeev Alur, Zisman Family Professor of Computer and Information Science Osbert Bastani, Research Assistant Professor of Computer and Information Science Steve Zdancewic, Professor of Computer and Information Science Le Song, Associate Professor in College of Computing, Georgia Institute of Technology LEARNING-AIDED PROGRAM SYNTHESIS AND VERIFICATION COPYRIGHT 2020 Xujie Si Licensed under a Creative Commons Attribution 4.0 License. To view a copy of this license, visit: http://creativecommons.org/licenses/by/4.0/ Dedicated to my parents and brothers. iii ACKNOWLEDGEMENTS First and foremost, I would like to thank my advisor, Mayur Naik, for providing a constant source of wisdom, guidance, and support over the six years of my Ph.D. journey. Were it not for his mentorship, I would not be here today. My thesis committee consisted of Rajeev Alur, Osbert Bastani, Steve Zdancewic, and Le Song: I thank them for the careful reading of this document and suggestions for improvement. In addition to providing valuable feedback on this dissertation, they have also provided extremely helpful advice over the years on research, com- munication, networking, and career planning. I would like to thank all my collaborators, particularly Hanjun Dai, Mukund Raghothaman, and Xin Zhang, with whom I have had numerous fruitful discus- sions, which finally lead to this thesis.
    [Show full text]
  • (12) United States Patent (10) Patent No.: US 8,341,602 B2 Hawblitzel Et Al
    USOO83416O2B2 (12) United States Patent (10) Patent No.: US 8,341,602 B2 Hawblitzel et al. (45) Date of Patent: Dec. 25, 2012 (54) AUTOMATED VERIFICATION OF A 7.65 E: $39. St. 727 TYPE-SAFE OPERATING SYSTEM 7,818,729- W - B1 * 10/2010 PlumOTley, et al.JT. .......... T17,140. 8, 104,021 B2* 1/2012 Erli tal. T17,126 (75) Inventors: Chris Hawblitzel, Redmond, WA (US); 8,127,280 B2 * 2/2012 E. al T17.136 Jean Yang, Cambridge, MA (US) 8,132,002 B2 * 3/2012 Lo et al. ......... ... 713, 164 8, 181,021 B2 * 5/2012 Ginter et al. .................. T13, 164 (73) Assignee: Microsoft Corporation, Redmond, WA 2004/0172638 A1 9, 2004 Larus (US) 2005, OO65973 A1 3/2005 Steensgaard et al. 2005, 0071387 A1 3, 2005 Mitchell (*) Notice: Subject to any disclaimer, the term of this (Continued) patent is extended or adjusted under 35 U.S.C. 154(b) by 442 days. OTHER PUBLICATIONS Klein et al., seL4: formal verification of an OS kernel, Oct. 2009, 14 (21) Appl. No.: 12/714,468 pages, <http://delivery.acm.org/10.1145/1630000/1629596.p207 klein.pdf>.* (22) Filed: Feb. 27, 2010 (Continued) (65) Prior Publication Data US 2010/O192130 A1 Jul 29, 2010 Primary Examiner — Thuy Dao ul. Z9, (74) Attorney, Agent, or Firm — Lyon & Harr, LLP; Mark A. Related U.S. Application Data Watson (63) Continuation-in-part of application No. 12/362.444, (57) ABSTRACT filed on Jan. 29, 2009. An Automated, Static Safety Verifier uses typed assembly 51) Int. C language (TAL) and Hoare logic to achieve highly automated, (51) o,F o/44 2006.O1 static verification of type and memory safety of an operating ( .01) system (OS).
    [Show full text]
  • Principles of Security and Trust
    Flemming Nielson David Sands (Eds.) Principles of Security LNCS 11426 ARCoSS and Trust 8th International Conference, POST 2019 Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019 Prague, Czech Republic, April 6–11, 2019, Proceedings Lecture Notes in Computer Science 11426 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board Members David Hutchison, UK Takeo Kanade, USA Josef Kittler, UK Jon M. Kleinberg, USA Friedemann Mattern, Switzerland John C. Mitchell, USA Moni Naor, Israel C. Pandu Rangan, India Bernhard Steffen, Germany Demetri Terzopoulos, USA Doug Tygar, USA Advanced Research in Computing and Software Science Subline of Lecture Notes in Computer Science Subline Series Editors Giorgio Ausiello, University of Rome ‘La Sapienza’, Italy Vladimiro Sassone, University of Southampton, UK Subline Advisory Board Susanne Albers, TU Munich, Germany Benjamin C. Pierce, University of Pennsylvania, USA Bernhard Steffen, University of Dortmund, Germany Deng Xiaotie, Peking University, Beijing, China Jeannette M. Wing, Microsoft Research, Redmond, WA, USA More information about this series at http://www.springer.com/series/7410 Flemming Nielson • David Sands (Eds.) Principles of Security and Trust 8th International Conference, POST 2019 Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019 Prague, Czech Republic, April 6–11, 2019 Proceedings Editors Flemming Nielson David Sands Technical University of Denmark Chalmers University of Technology Kongens Lyngby, Denmark Gothenburg, Sweden ISSN 0302-9743 ISSN 1611-3349 (electronic) Lecture Notes in Computer Science ISBN 978-3-030-17137-7 ISBN 978-3-030-17138-4 (eBook) https://doi.org/10.1007/978-3-030-17138-4 Library of Congress Control Number: 2019936300 LNCS Sublibrary: SL4 – Security and Cryptology © The Editor(s) (if applicable) and The Author(s) 2019.
    [Show full text]
  • LNCS 8141 Molecular Programming 19Th International Conference, DNA 19 Tempe, AZ, USA, September 2013 Proceedings
    David Soloveichik Bernard Yurke (Eds.) DNA Computing and LNCS 8141 Molecular Programming 19th International Conference, DNA 19 Tempe, AZ, USA, September 2013 Proceedings 123 Lecture Notes in Computer Science 8141 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Germany Madhu Sudan Microsoft Research, Cambridge, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbruecken, Germany David Soloveichik Bernard Yurke (Eds.) DNA Computing and Molecular Programming 19th International Conference, DNA 19 Tempe, AZ, USA, September 22-27, 2013 Proceedings 13 Volume Editors David Soloveichik University of California, San Francisco Center for Systems and Synthetic Biology 1700 4th Street San Francisco, CA 94158, USA E-mail: [email protected] Bernard Yurke Boise State University
    [Show full text]
  • Applied Type System: an Approach to Practical Programming with Theorem-Proving
    ZU064-05-FPR main 15 January 2016 12:51 Under consideration for publication in J. Functional Programming 1 Applied Type System: An Approach to Practical Programming with Theorem-Proving Hongwei Xi∗ Boston University, Boston, MA 02215, USA (e-mail: [email protected]) Abstract The framework Pure Type System (PTS) offers a simple and general approach to designing and formalizing type systems. However, in the presence of dependent types, there often exist certain acute problems that make it difficult for PTS to directly accommodate many common realistic programming features such as general recursion, recursive types, effects (e.g., exceptions, refer- ences, input/output), etc. In this paper, Applied Type System (ATS) is presented as a framework for designing and formalizing type systems in support of practical programming with advanced types (including dependent types). In particular, it is demonstrated that ATS can readily accommodate a paradigm referred to as programming with theorem-proving (PwTP) in which programs and proofs are constructed in a syntactically intertwined manner, yielding a practical approach to internalizing constraint-solving needed during type-checking. The key salient feature of ATS lies in a complete separation between statics, where types are formed and reasoned about, and dynamics, where pro- grams are constructed and evaluated. With this separation, it is no longer possible for a program to occur in a type as is otherwise allowed in PTS. The paper contains not only a formal development of ATS but also some examples taken from ATS, a programming language with a type system rooted in ATS, in support of using ATS as a framework to form type systems for practical programming.
    [Show full text]
  • Homework: Verification
    Homework: Verification The goal of this assignment is to build a simple program verifier. The support code includes a parser and abstract syntax for a simple language of imperative commands, which should be the input language of your verifier. You will write a function to calculate weakest preconditions and verify that user-written assertions and loop invariants are correct using the Z3 Theorem Prover. 1 Restrictions None. 2 Setup To do this assignment, you will need a copy of the Z3 Theorem Prover: https://github.com/Z3Prover/z3/releases The packages on the website include Z3 bindings for several languages. However, you will only need the z3 executable. (In particular, you do not need the OCaml bindings for Z3.) We’ve written an OCaml library that let’s you interface with Z3 that you can install using OPAM: opam install ocaml-z3 3 Requirements Write a program that takes one argument: verif.d.byte program The argument program should be the name of a file that contains a program written using the grammer in fig. 23.1. Your verifier should verify that the pre- and post- conditions of the program (i.e., the predicates prefixed by requires and ensures) are valid and terminate with exit code 0. If the are invalid, your verifier should terminate with a non-zero exit code. Feel free to output whatever you need on standard in / standard error to help you debug and understand your verifier. 4 Support Code The module Imp defines the abstract syntax of the language shown in fig. 23.1 and includes functions to parse programs in the language.
    [Show full text]
  • COIN Attacks: on Insecurity of Enclave Untrusted Interfaces In
    Session 11A: Enclaves and memory security — Who will guard the guards? COIN Attacks: On Insecurity of Enclave Untrusted Interfaces in SGX Mustakimur Rahman Khandaker Yueqiang Cheng [email protected] [email protected] Florida State University Baidu Security Zhi Wang Tao Wei [email protected] [email protected] Florida State University Baidu Security Abstract Keywords. Intel SGX; enclave; vulnerability detection Intel SGX is a hardware-based trusted execution environ- ACM Reference Format: ment (TEE), which enables an application to compute on Mustakimur Rahman Khandaker, Yueqiang Cheng , Zhi Wang, confidential data in a secure enclave. SGX assumes apow- and Tao Wei. 2020. COIN Attacks: On Insecurity of Enclave Un- erful threat model, in which only the CPU itself is trusted; trusted Interfaces in SGX. In Proceedings of the Twenty-Fifth In- anything else is untrusted, including the memory, firmware, ternational Conference on Architectural Support for Programming system software, etc. An enclave interacts with its host ap- Languages and Operating Systems (ASPLOS ’20), March 16–20, 2020, Lausanne, Switzerland. ACM, New York, NY, USA, 15 pages. https: plication through an exposed, enclave-specific, (usually) bi- //doi.org/10.1145/3373376.3378486 directional interface. This interface is the main attack surface of the enclave. The attacker can invoke the interface in any 1 Introduction order and inputs. It is thus imperative to secure it through careful design and defensive programming. Intel Software Guard Extensions (SGX) introduces a set of In this work, we systematically analyze the attack models ISA extensions to enable a trusted execution environment, against the enclave untrusted interfaces and summarized called enclave, for security-sensitive computations in user- them into the COIN attacks – Concurrent, Order, Inputs, and space processes.
    [Show full text]
  • Gray-Box Monitoring of Hyperproperties?
    Gray-box Monitoring of Hyperproperties? Sandro Stucki1[0000−0001−5608−8273], César Sánchez2[0000−0003−3927−4773], Gerardo Schneider1[0000−0003−0629−6853], and Borzoo Bonakdarpour3[0000−0003−1800−5419] 1 University of Gothenburg, Sweden, [email protected],[email protected] 2 IMDEA Software Institute, Spain, [email protected] 3 Iowa State University, USA, [email protected] Abstract. Many important system properties, particularly in security and privacy, cannot be verified statically. Therefore, runtime verification is an appealing alternative. Logics for hyperproperties, such as Hyper- LTL, support a rich set of such properties. We first show that black-box monitoring of HyperLTL is in general unfeasible, and suggest a gray-box approach. Gray-box monitoring implies performing analysis of the system at run-time, which brings new limitations to monitorabiliy (the feasibility of solving the monitoring problem). Thus, as another contribution of this paper, we refine the classic notions of monitorability, both for trace prop- erties and hyperproperties, taking into account the computability of the monitor. We then apply our approach to monitor a privacy hyperproperty called distributed data minimality, expressed as a HyperLTL property, by using an SMT-based static verifier at runtime. 1 Introduction Consider a confidentiality policy ' that requires that every pair of separate executions of a system agree on the position of occurrences of some proposition a. Otherwise, an external observer may learn some sensitive information about the system. We are interested in studying how to build runtime monitors for properties like ', where the monitor receives independent executions of the system under scrutiny and intend to determine whether or not the system satisfies the property.
    [Show full text]