Browsing by Author "Vardi, Moshe Y"

Now showing 1 - 9 of 9
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    A Constraint-Based Approach to Reactive Task and Motion Planning
    (2016-01-26) Wang, Yue; Chaudhuri, Swarat; Kavraki, Lydia E; Vardi, Moshe Y
    This thesis presents a novel and scalable approach for Reactive Task and Motion Planning. We consider changing environments with uncontrollable agents, where the robot needs a policy to respond correctly in the infinite interaction with the environment. Our approach operates on task and motion domains that combine actions over discrete states with continuous, collision-free paths. We synthesize a policy by iteratively verifying and searching for a policy candidate. For efficient verification, we employ Satisfiability Modulo Theories (SMT) solvers using a new extension of proof rules for Temporal Property Verification. For efficient policy search, we apply domain-specific heuristics to generalize verification failures. Furthermore, the SMT solver enables quantitative specifications such as energy limits. We benchmark our policy synthesizer in a mobile manipulation domain, showing that our approach offers better scalability compared to a state-of-the-art robotic synthesis tool in the tested benchmarks and demonstrating order-of-magnitude speedup from our heuristics.
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    Automated OS-level Device Runtime Power Management
    (2014-12-01) Xu, Chao; Zhong, Lin; Cavallaro, Joseph R; Vardi, Moshe Y; Wallach, Dan S
    Hardware devices on a modern System-on-Chip (SoC), ranging from accelerators to IO controllers, usually account for the largest portion of the chip area. It is therefore vital for Operating Systems (OS) to disable and enable these devices at run time, so that idle devices can enter low-power state timely while meeting user’s performance expectation. This is called device runtime Power Management (PM), for which individual device drivers in commodity OSes are held responsible. Based on the observations of existing drivers and their evolution, we consider counting on drivers for device runtime PM harmful. We identify three pieces of information essential to device runtime PM, and show that all of them can be obtained without involving drivers, either by using a software inference approach atop existing ARM-based SoC, or more efficiently, by adding one register bit to each device. We thus argue for a structural change to the current Linux runtime PM framework, replacing PM code in each individual driver with one kernel module called central PM agent. We experimentally show that central PM agent is just as effective as hand-tuned driver PM code. We also present a software tool called PowerAdvisor, as a remedy to simplify driver PM efforts without overhauling the current Linux runtime PM framework. PowerAdvisor analyzes trace generated from historic executions and suggests PM calls to be inserted at certain driver source locations. Although a best-effort tool, PowerAdvisor not only reproduces hand-tuned PM code that already exists in stock drivers, but also correctly suggests PM code never known before . Overall, our experiences show that it is promising to ultimately free driver developers from manual PM.
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    Domain-Driven Approaches for Constrained Counting and Sampling
    (2021-12-16) Shrotri, Aditya Aniruddha; Vardi, Moshe Y
    Constrained Counting and Sampling are two fundamental problems in Computer Science, where the task is to count the number of solutions or satisfying assignments to a given set of constraints, or to sample a solution uniformly at random. Counting and sampling along with their approximate and weighted variants have been extensively studied in both theory and practice. However, this research effort has been disjointed, resulting in significant gaps in knowledge. On one hand, algorithms with worst-case polynomial running times are considered to be the gold standard by the theory community, but rarely scale well in practice. On the other hand, powerful general-purpose algorithms and tools developed by the AI and Formal Methods communities often fail to scale on ‘easy’ problems with polynomial upper bounds. The goal of this dissertation is to illuminate and address this disconnect. Specifically, we develop flexible techniques that natively exploit the structure inherent in domain-specific constraints. This often leads to significant performance gains over the popular approach which attempts to shoehorn all constraints to fit a rigid algorithm. Motivated by numerous practical applications and a lack of practically scalable tools with strong theoretical guarantees, we present new solutions for the concrete problems of DNF-Counting, conditional counting, computing the matrix permanent, sampling traces of a transition system and weighted sampling from low-treewidth CNF formulas. Our empirical analyses reveal a nuanced picture wherein our approaches are seen to be a valuable addition to an algorithmic portfolio.
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    Evaluating Performance of Automaton University Checking Algorithms
    (2019-03-28) Fisher, Corey Scott; Vardi, Moshe Y
    NFA universality is an important problem in formal verification, since it is an effective proxy for complementation of NFAs - a key operation that underlies most verification algorithms. However, because complemented automata are extremely large, many modern tools use symbolic representations to perform complementation and universality checking. One state-of-the-art tool for NFA universality, ALASKA, symbolically represents automata using binary decision diagrams (BDDs) to more efficiently complement them with the subset construction. The algorithm usually only represents a small number of subset-constructed states at a time, relative to the vast state space. Zero-suppressed decision diagrams (ZDDs) have the same semantics as BDDs, but are more efficient when representing sparse solution sets. We used this advantage in constructing a new ZDD-based tool, ALASKA-ZDD, which completely replaces ALASKA's symbolic representation with a ZDD-based one. We then experimentally compared it with ALASKA, using random automata generated with the widely-used Tabakov-Vardi (T-V) random model due to a lack of practical benchmarks. We found that ALASKA-ZDD is more efficient on automata with sparse transition relations. But how do we know the T-V model gives robust results? The model was originally adopted due to lack of practical benchmarks, but this also prevents checking its reliability against real examples. While it statistically guarantees certain universality properties about the automata it produces, no further work has been done to verify its results. Therefore, it is unclear if tests on the T-V model are sufficient. In graph theory, many different random models are used for representing different problems - would that be an appropriate approach for verification? We introduce three new random models, and show that their results for the NFA universality question are the same as T-V. We also compare multiple solutions to the Buechi universality problem on these models, and find that their results are the same as T-V. Therefore, in addition to showing ALASKA-ZDD is competitive, we show that T-V can be used as a robust random model for verification, across multiple problems, verifying many previous results with the model.
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    FPRAS Approximation of the Matrix Permanent in Practice
    (2020-06-12) Newman, James; Vardi, Moshe Y
    The matrix permanent belongs to the complexity class #P-Complete. It is gener- ally believed to be computationally infeasible for large problem sizes, and significant research has been done on approximation algorithms for the matrix permanent. We present an implementation and detailed runtime analysis of one such Markov Chain Monte Carlo (MCMC) based Fully Polynomial Randomized Approximation Scheme (FPRAS) for the matrix permanent which has previously only been described theo- retically and with big-Oh runtime analysis. We demonstrate that the constant factors hidden by the big-Oh analysis result in computational infeasibility. We explore the performance of the FPRAS implementation under relaxed sampling parameters to gauge the room for improvement in the probabilistic analysis of sampling parameter requirements for the FPRAS.
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    On Hashing-Based Approaches to Approximate DNF-Counting
    (2017-11-07) Shrotri, Aditya Aniruddha; Vardi, Moshe Y
    Propositional model counting is a fundamental problem in AI. For DNF formulas, Monte Carlo-based techniques provide a fully polynomial randomized approximation scheme (FPRAS). For CNF constraints, hashing-based techniques are highly successful. It was recently shown that hashing techniques also yield an FPRAS for DNF counting. Our analysis, however, shows that the proposed hashing approach provides poor time complexity compared to the Monte Carlo techniques, for DNF Counting. Given the success of hashing techniques for CNF constraints, it is natural to ask: Can hashing techniques provide an efficient FPRAS for DNF counting? We provide a positive answer to this question. We introduce two novel algorithmic techniques: Symbolic Hashing and Stochastic Cell Counting, and a new family of Row-Echelon hash functions. We design a hashing-based FPRAS of similar complexity (up to polylog factors) as that of prior works. We also provide an empirical comparison of the various approaches.
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    Random CNF-XOR Formulas
    (2017-04-21) Dudek, Jeffrey M; Vardi, Moshe Y
    Boolean Satisfiability (SAT) is fundamental in many diverse areas such as artificial intelligence, formal verification, and biology. Recent universal-hashing based approaches to the problems of sampling and counting crucially depend on the runtime performance of specialized SAT solvers on formulas expressed as the conjunction of both k-CNF constraints and variable-width XOR constraints (known as CNF-XOR formulas), but random CNF-XOR formulas are unexplored in prior work. In this work, we present the first study of random CNF-XOR formulas. We prove that a phase-transition in the satisfiability of random CNF-XOR formulas exists for k=2 and (when the number of k-CNF constraints is small) for k>2. We empirically demonstrate that a state-of-the-art SAT solver scales exponentially on random CNF-XOR formulas across many clause densities, peaking around the empirical phase-transition location. Finally, we prove that the solution space of random CNF-XOR formulas 'shatters' at all nonzero XOR-clause densities into well-separated components.
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    Robot Manipulation Planning Under Linear Temporal Logic Specifications
    (2015-12-07) He, Keliang; Kavraki, Lydia E; Vardi, Moshe Y; Chaudhuri, Swarat
    Automated planning for manipulation tasks is highly desirable, for it enables robot manipulators to be used by none robotics experts. This thesis presents one approach to solving manipulation planning for tasks expressed in linear temporal logic (ltl). This approach is based on the synergistic framework, which provides probabilistic completeness guarantees. Even though the synergistic framework has shown to work well for planning for ltl tasks in the navigation domain, it lacked an abstraction that can capture the high dimensionality of manipulation. This thesis enables manipulation planning using the synergistic framework by introducing a manipulation abstraction and modifying the interaction between task and motion planning in the framework. The modified framework is shown to be effectively in case studies in both simulation and physical systems. The case studies also show that the synergistic framework plans for manipulation problems more effective using the manipulation abstraction in comparison with a naive abstraction.
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    Solving Hybrid Boolean Constraints by Fourier Expansions and Continuous Optimization
    (2020-06-04) Zhang, Zhiwei; Vardi, Moshe Y
    The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side---especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers---has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF), have become quite mature, SAT solvers that are effective on other types of constraints (e.g., cardinality constraints and XORs) are less well studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time. To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Due to characteristics of multilinear polynomials, this method owns some interesting theoretical guarantees. Empirical results demonstrate that a proof-of-concept implementation of FourierSAT combined with engineering tricks is more robust than other solvers on certain classes of benchmarks. We believe this work is a promising start of a new line of research on Boolean SAT and MaxSAT.