Trading Determinism for Time in Space Bounded Computations

Savitch showed in $1970$ that nondeterministic logspace (NL) is contained in deterministic $\mathcal{O}(\log^2 n)$ space but his algorithm requires quasipolynomial time. The question whether we can have a deterministic algorithm for every problem in NL that requires polylogarithmic space and simultaneously runs in polynomial time was left open. In this paper we give a partial solution to this problem and show that for every language in NL there exists an unambiguous nondeterministic algorithm that requires $\mathcal{O}(\log^2 n)$ space and simultaneously runs in polynomial time.Comment: Accepted in MFCS 201

Alternation-Trading Proofs, Linear Programming, and Lower Bounds

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT, Majority-of-Majority-SAT, and Tautologies, to name a few. The proofs of these lower bounds follow a certain proof-by-contradiction strategy that we call alternation-trading. An important open problem is to determine how powerful such proofs can possibly be. We propose a methodology for studying these proofs that makes them amenable to both formal analysis and automated theorem proving. We prove that the search for better lower bounds can often be turned into a problem of solving a large series of linear programming instances. Implementing a small-scale theorem prover based on this result, we extract new human-readable time lower bounds for several problems. This framework can also be used to prove concrete limitations on the current techniques.Comment: To appear in STACS 2010, 12 page

Locality and Singularity for Store-Atomic Memory Models

Robustness is a correctness notion for concurrent programs running under relaxed consistency models. The task is to check that the relaxed behavior coincides (up to traces) with sequential consistency (SC). Although computationally simple on paper (robustness has been shown to be PSPACE-complete for TSO, PGAS, and Power), building a practical robustness checker remains a challenge. The problem is that the various relaxations lead to a dramatic number of computations, only few of which violate robustness. In the present paper, we set out to reduce the search space for robustness checkers. We focus on store-atomic consistency models and establish two completeness results. The first result, called locality, states that a non-robust program always contains a violating computation where only one thread delays commands. The second result, called singularity, is even stronger but restricted to programs without lightweight fences. It states that there is a violating computation where a single store is delayed. As an application of the results, we derive a linear-size source-to-source translation of robustness to SC-reachability. It applies to general programs, regardless of the data domain and potentially with an unbounded number of threads and with unbounded buffers. We have implemented the translation and verified, for the first time, PGAS algorithms in a fully automated fashion. For TSO, our analysis outperforms existing tools

An Approach to Computational Complexity in Membrane Computing

In this paper we present a theory of computational complexity in the framework of membrane computing. Polynomial complexity classes in recognizer membrane systems and capturing the classical deterministic and non-deterministic modes of computation, are introduced. In this context, a characterization of the relation P = NP is described.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

Easiness Amplification and Uniform Circuit Lower Bounds

We present new consequences of the assumption that time-bounded algorithms can be "compressed" with non-uniform circuits. Our main contribution is an "easiness amplification" lemma for circuits. One instantiation of the lemma says: if n^{1+e}-time, tilde{O}(n)-space computations have n^{1+o(1)} size (non-uniform) circuits for some e > 0, then every problem solvable in polynomial time and tilde{O}(n) space has n^{1+o(1)} size (non-uniform) circuits as well. This amplification has several consequences: * An easy problem without small LOGSPACE-uniform circuits. For all e > 0, we give a natural decision problem, General Circuit n^e-Composition, that is solvable in about n^{1+e} time, but we prove that polynomial-time and logarithmic-space preprocessing cannot produce n^{1+o(1)}-size circuits for the problem. This shows that there are problems solvable in n^{1+e} time which are not in LOGSPACE-uniform n^{1+o(1)} size, the first result of its kind. We show that our lower bound is non-relativizing, by exhibiting an oracle relative to which the result is false. * Problems without low-depth LOGSPACE-uniform circuits. For all e > 0, 1 < d < 2, and e < d we give another natural circuit composition problem computable in tilde{O}(n^{1+e}) time, or in O((log n)^d) space (though not necessarily simultaneously) that we prove does not have SPACE[(log n)^e]-uniform circuits of tilde{O}(n) size and O((log n)^e) depth. We also show SAT does not have circuits of tilde{O}(n) size and log^{2-o(1)}(n) depth that can be constructed in log^{2-o(1)}(n) space. * A strong circuit complexity amplification. For every e > 0, we give a natural circuit composition problem and show that if it has tilde{O}(n)-size circuits (uniform or not), then every problem solvable in 2^{O(n)} time and 2^{O(sqrt{n log n})} space (simultaneously) has 2^{O(sqrt{n log n})}-size circuits (uniform or not). We also show the same consequence holds assuming SAT has tilde{O}(n)-size circuits. As a corollary, if n^{1.1} time computations (or O(n) nondeterministic time computations) have tilde{O}(n)-size circuits, then all problems in exponential time and subexponential space (such as quantified Boolean formulas) have significantly subexponential-size circuits. This is a new connection between the relative circuit complexities of easy and hard problems

Metastability-Containing Circuits

In digital circuits, metastability can cause deteriorated signals that neither are logical 0 or logical 1, breaking the abstraction of Boolean logic. Unfortunately, any way of reading a signal from an unsynchronized clock domain or performing an analog-to-digital conversion incurs the risk of a metastable upset; no digital circuit can deterministically avoid, resolve, or detect metastability (Marino, 1981). Synchronizers, the only traditional countermeasure, exponentially decrease the odds of maintained metastability over time. Trading synchronization delay for an increased probability to resolve metastability to logical 0 or 1, they do not guarantee success. We propose a fundamentally different approach: It is possible to contain metastability by fine-grained logical masking so that it cannot infect the entire circuit. This technique guarantees a limited degree of metastability in---and uncertainty about---the output. At the heart of our approach lies a time- and value-discrete model for metastability in synchronous clocked digital circuits. Metastability is propagated in a worst-case fashion, allowing to derive deterministic guarantees, without and unlike synchronizers. The proposed model permits positive results and passes the test of reproducing Marino's impossibility results. We fully classify which functions can be computed by circuits with standard registers. Regarding masking registers, we show that they become computationally strictly more powerful with each clock cycle, resulting in a non-trivial hierarchy of computable functions

Mechanisms for Outsourcing Computation via a Decentralized Market

As the number of personal computing and IoT devices grows rapidly, so does the amount of computational power that is available at the edge. Since many of these devices are often idle, there is a vast amount of computational power that is currently untapped, and which could be used for outsourcing computation. Existing solutions for harnessing this power, such as volunteer computing (e.g., BOINC), are centralized platforms in which a single organization or company can control participation and pricing. By contrast, an open market of computational resources, where resource owners and resource users trade directly with each other, could lead to greater participation and more competitive pricing. To provide an open market, we introduce MODiCuM, a decentralized system for outsourcing computation. MODiCuM deters participants from misbehaving-which is a key problem in decentralized systems-by resolving disputes via dedicated mediators and by imposing enforceable fines. However, unlike other decentralized outsourcing solutions, MODiCuM minimizes computational overhead since it does not require global trust in mediation results. We provide analytical results proving that MODiCuM can deter misbehavior, and we evaluate the overhead of MODiCuM using experimental results based on an implementation of our platform

The HdpH DSLs for scalable reliable computation

The statelessness of functional computations facilitates both parallelism and fault recovery. Faults and non-uniform communication topologies are key challenges for emergent large scale parallel architectures. We report on HdpH and HdpH-RS, a pair of Haskell DSLs designed to address these challenges for irregular task-parallel computations on large distributed-memory architectures. Both DSLs share an API combining explicit task placement with sophisticated work stealing. HdpH focuses on scalability by making placement and stealing topology aware whereas HdpH-RS delivers reliability by means of fault tolerant work stealing. We present operational semantics for both DSLs and investigate conditions for semantic equivalence of HdpH and HdpH-RS programs, that is, conditions under which topology awareness can be transparently traded for fault tolerance. We detail how the DSL implementations realise topology awareness and fault tolerance. We report an initial evaluation of scalability and fault tolerance on a 256-core cluster and on up to 32K cores of an HPC platform

Speculation in Parallel and Distributed Event Processing Systems

Event stream processing (ESP) applications enable the real-time processing of continuous flows of data. Algorithmic trading, network monitoring, and processing data from sensor networks are good examples of applications that traditionally rely upon ESP systems. In addition, technological advances are resulting in an increasing number of devices that are network enabled, producing information that can be automatically collected and processed. This increasing availability of on-line data motivates the development of new and more sophisticated applications that require low-latency processing of large volumes of data. ESP applications are composed of an acyclic graph of operators that is traversed by the data. Inside each operator, the events can be transformed, aggregated, enriched, or filtered out. Some of these operations depend only on the current input events, such operations are called stateless. Other operations, however, depend not only on the current event, but also on a state built during the processing of previous events. Such operations are, therefore, named stateful. As the number of ESP applications grows, there are increasingly strong requirements, which are often difficult to satisfy. In this dissertation, we address two challenges created by the use of stateful operations in a ESP application: (i) stateful operators can be bottlenecks because they are sensitive to the order of events and cannot be trivially parallelized by replication; and (ii), if failures are to be tolerated, the accumulated state of an stateful operator needs to be saved, saving this state traditionally imposes considerable performance costs. Our approach is to evaluate the use of speculation to address these two issues. For handling ordering and parallelization issues in a stateful operator, we propose a speculative approach that both reduces latency when the operator must wait for the correct ordering of the events and improves throughput when the operation in hand is parallelizable. In addition, our approach does not require that user understand concurrent programming or that he or she needs to consider out-of-order execution when writing the operations. For fault-tolerant applications, traditional approaches have imposed prohibitive performance costs due to pessimistic schemes. We extend such approaches, using speculation to mask the cost of fault tolerance.:1 Introduction 1 1.1 Event stream processing systems ......................... 1 1.2 Running example ................................. 3 1.3 Challenges and contributions ........................... 4 1.4 Outline ...................................... 6 2 Background 7 2.1 Event stream processing ............................. 7 2.1.1 State in operators: Windows and synopses ............................ 8 2.1.2 Types of operators ............................ 12 2.1.3 Our prototype system........................... 13 2.2 Software transactional memory.......................... 18 2.2.1 Overview ................................. 18 2.2.2 Memory operations............................ 19 2.3 Fault tolerance in distributed systems ...................................... 23 2.3.1 Failure model and failure detection ...................................... 23 2.3.2 Recovery semantics............................ 24 2.3.3 Active and passive replication ...................... 24 2.4 Summary ..................................... 26 3 Extending event stream processing systems with speculation 27 3.1 Motivation..................................... 27 3.2 Goals ....................................... 28 3.3 Local versus distributed speculation ....................... 29 3.4 Models and assumptions ............................. 29 3.4.1 Operators................................. 30 3.4.2 Events................................... 30 3.4.3 Failures .................................. 31 4 Local speculation 33 4.1 Overview ..................................... 33 4.2 Requirements ................................... 35 4.2.1 Order ................................... 35 4.2.2 Aborts................................... 37 4.2.3 Optimism control ............................. 38 4.2.4 Notifications ............................... 39 4.3 Applications.................................... 40 4.3.1 Out-of-order processing ......................... 40 4.3.2 Optimistic parallelization......................... 42 4.4 Extensions..................................... 44 4.4.1 Avoiding unnecessary aborts ....................... 44 4.4.2 Making aborts unnecessary........................ 45 4.5 Evaluation..................................... 47 4.5.1 Overhead of speculation ......................... 47 4.5.2 Cost of misspeculation .......................... 50 4.5.3 Out-of-order and parallel processing micro benchmarks ........... 53 4.5.4 Behavior with example operators .................... 57 4.6 Summary ..................................... 60 5 Distributed speculation 63 5.1 Overview ..................................... 63 5.2 Requirements ................................... 64 5.2.1 Speculative events ............................ 64 5.2.2 Speculative accesses ........................... 69 5.2.3 Reliable ordered broadcast with optimistic delivery .................. 72 5.3 Applications .................................... 75 5.3.1 Passive replication and rollback recovery ................................ 75 5.3.2 Active replication ............................. 80 5.4 Extensions ..................................... 82 5.4.1 Active replication and software bugs ..................................... 82 5.4.2 Enabling operators to output multiple events ........................ 87 5.5 Evaluation .................................... 87 5.5.1 Passive replication ............................ 88 5.5.2 Active replication ............................. 88 5.6 Summary ..................................... 93 6 Related work 95 6.1 Event stream processing engines ......................... 95 6.2 Parallelization and optimistic computing ................................ 97 6.2.1 Speculation ................................ 97 6.2.2 Optimistic parallelization ......................... 98 6.2.3 Parallelization in event processing .................................... 99 6.2.4 Speculation in event processing ..................... 99 6.3 Fault tolerance .................................. 100 6.3.1 Passive replication and rollback recovery ............................... 100 6.3.2 Active replication ............................ 101 6.3.3 Fault tolerance in event stream processing systems ............. 103 7 Conclusions 105 7.1 Summary of contributions ............................ 105 7.2 Challenges and future work ............................ 106 Appendices Publications 107 Pseudocode for the consensus protocol 10