etd@IISc Collection:http://hdl.handle.net/2005/182017-07-29T01:49:26Z2017-07-29T01:49:26ZModule Grobner Bases Over Fields With ValuationSen, Aritrahttp://hdl.handle.net/2005/26442017-07-12T10:47:35Z2017-07-11T18:30:00ZTitle: Module Grobner Bases Over Fields With Valuation
Authors: Sen, Aritra
Abstract: Tropical geometry is an area of mathematics that interfaces algebraic geometry and combinatorics. The main object of study in tropical geometry is the tropical variety, which is the combinatorial counterpart of a classical variety. A classical variety is converted into a tropical variety by a process called tropicalization, thus reducing the problems of algebraic geometry to problems of combinatorics. This new tropical variety encodes several useful information about the original variety, for example an algebraic variety and its tropical counterpart have the same dimension.
In this thesis, we look at the some of the computational aspects of tropical algebraic geometry. We study a generalization of Grobner basis theory of modules which unlike the standard Grobner basis also takes the valuation of coefficients into account. This was rst introduced in (Maclagan & Sturmfels, 2009) in the settings of polynomial rings and its computational aspects were first studied in (Chan & Maclagan, 2013) for the polynomial ring case. The motivation for this comes from tropical geometry as it can be used to compute tropicalization of varieties. We further generalize this to the case of modules. But apart from that it has many other computational advantages. For example, in the standard case the size of the initial submodule generally grows with the increase in degree of the generators. But in this case, we give an example of a family of submodules where the size of the initial submodule remains constant. We also develop an algorithm for computation of Grobner basis of submodules of modules over Z=p`Z[x1; : : : ; xn] that works for any weight vector.
We also look at some of the important applications of this new theory. We show how this can be useful in efficiently solving the submodule membership problem. We also study the computation of Hilbert polynomials, syzygies and free resolutions.2017-07-11T18:30:00ZMechanism Design For Strategic CrowdsourcingNath, Swapravahttp://hdl.handle.net/2005/24972015-12-14T07:12:21Z2013-12-16T18:30:00ZTitle: Mechanism Design For Strategic Crowdsourcing
Authors: Nath, Swaprava
Abstract: This thesis looks into the economics of crowdsourcing using game theoretic modeling. The art of aggregating information and expertise from a diverse population has been in practice since a long time. The Internet and the revolution in communication and computational technologies have made this task easier and given birth to a new era of online resource aggregation, which is now popularly referred to as crowdsourcing. Two important features of this aggregation technique are: (a) crowdsourcing is always human driven, hence the participants are rational and intelligent, and they have a payoff function that they aim to maximize, and (b) the participants are connected over a social network which helps to reach out to a large set of individuals. To understand the behavior and the outcome of such a strategic crowd, we need to understand the economics of a crowdsourcing network. In this thesis, we have considered the following three major facets of the strategic crowdsourcing problem.
(i) Elicitation of the true qualities of the crowd workers: As the crowd is often unstructured and unknown to the designer, it is important to ensure if the crowdsourced job is indeed performed at the highest quality, and this requires elicitation of the true qualities which are typically the participants' private information.
(ii) Resource critical task execution ensuring the authenticity of both the information and the identity of the participants: Due to the diverse geographical, cultural, socio-economic reasons, crowdsourcing entails certain manipulations that are unusual in the classical theory. The design has to be robust enough to handle fake identities or incorrect information provided by the crowd while performing crowdsourcing contests.
(iii) Improving the productive output of the crowdsourcing network: As the designer's goal is to maximize a certain measurable output of the crowdsourcing system, an interesting question is how one can design the incentive scheme and/or the network so that the system performs at an optimal level taking into account the strategic nature of the individuals. In the thesis, we design novel mechanisms to solve the problems above using game theoretic modeling. Our investigation helps in understanding certain limits of achievability, and provides design protocols in order to make crowdsourcing more reliable, effective, and productive.2013-12-16T18:30:00ZModel-Checking Infinite-State Systems For Information Flow Security PropertiesRaghavendra, K Rhttp://hdl.handle.net/2005/26012017-02-16T10:26:10Z2017-02-15T18:30:00ZTitle: Model-Checking Infinite-State Systems For Information Flow Security Properties
Authors: Raghavendra, K R
Abstract: Information flow properties are away of specifying security properties of systems ,dating back to the work of Goguen and Meseguer in the eighties. In this framework ,a system is modeled as having high-level (or confidential)events as well as low-level (or public) events, and a typical property requires that the high-level events should not “influence ”the occurrence of low-level events. In other words, the sequence of low-level events observed from a system execution should not reveal “too much” information about the high-level events that may have taken place. For example, the trace-based “non-inference” property states that for every trace produced by the system, its projection to low-level events must also be a possible trace of the system. For a system satisfying non-inference, a low-level adversary (who knows the language generated by the system) viewing only the low-level events in any execution cannot infer any in-formation about the occurrence of high-level events in that execution. Other well-known properties include separability, generalized non-interference, non-deducibility of outputs etc. These properties are trace-based. Similarly there is another class of properties based on the structure of the transition system called bisimulation-based information flow properties, defined by Focardiand Gorrieriin1995.
In our thesis we study the problem of model-checking the well-known trace-based and bisimulation-based properties for some popular classes of infinite-state system models. We first consider trace-based properties. We define some language-theoretic operations that help to characterize language-inclusion in terms of satisfaction of these properties. This gives us a reduction of the language inclusion problem for a class of system models, say F, to the model-checking problem for F, whenever F, is effectively closed under these language-theoretic operations. We apply this result to show that the model-checking problem for Petri nets, push down systems and for some properties on deterministic push down systems is undecidable. We also consider the class of visibly pushdown systems and show that their model-checking problem is undecidable in general(for some properties).Then we show that for the restricted class of visibly pushdown systems in which all the high (confidential) event are internal, the model-checking problem becomes decidable. Similarly we show that the problem of model-checking bisimulation-based properties is undecidable for Petrinets, pushdown systems and process algebras.
Next we consider the problem of detecting information leakage in programs. Here the programs are modeled to have low and high inputs and low outputs. The well known definition of“ non-interference” on programs says that in no execution should the low outputs depend on the high inputs. However this definition was shown to be too strong to be used in practice, with a simple(and considered to be safe)“password-checking” program failing it.“Abstract non-interference(ANI)”and its variants were proposed in the literature to generalize or weaken non-interference. We call these definitions qualitative refinements of non-interference. We study the problem of model-checking many classes of finite-data programs(variables taking values from a bounded domain)for these refinements. We give algorithms and show that this problem is in PSPACE for while, EXPTIME for recursive and EXPSPACE for asynchronous finite-data programs.
We finally study different quantitative refinements of non-interference pro-posed in the literature. We first characterize these measures in terms of pre images. These characterizations potentially help designing analysis computing over and under approximations for these measures. Then we investigate the applicability of these measures on standard cryptographic functions.2017-02-15T18:30:00ZTiling Stencil Computations To Maximize ParallelismBandishti, Vinayaka Prakashahttp://hdl.handle.net/2005/26192017-05-21T11:42:33Z2017-05-20T18:30:00ZTitle: Tiling Stencil Computations To Maximize Parallelism
Authors: Bandishti, Vinayaka Prakasha
Abstract: Stencil computations are iterative kernels often used to simulate the change in a discretized spatial domain overtime (e.g., computational fluid dynamics) or to solve for unknowns in a discretized space by converging to a steady state (i.e., partial differential equations).They are commonly found in many scientific and engineering applications. Most stencil computations allow tile-wise concurrent start ,i.e., there exists a face of the iteration space and a set of tiling hyper planes such that all tiles along that face can be started concurrently. This provides load balance and maximizes parallelism.
Loop tiling is a key transformation used to exploit both data locality and parallelism from stencils simultaneously. Numerous works exist that target improving locality, controlling frequency of synchronization, and volume of communication wherever applicable. But, concurrent start-up of tiles that evidently translates into perfect load balance and often reduction in frequency of synchronization is completely ignored. Existing automatic tiling frameworks often choose hyperplanes that lead to pipelined start-up and load imbalance. We address this issue with a new tiling technique that ensures concurrent start-up as well as perfect load balance whenever possible. We ﬁrst provide necessary and sufficient conditions on tiling hyperplanes to enable concurrent start for programs with affine data accesses. We then discuss an iterative approach to find such hyperplanes.
It is not possible to directly apply automatic tiling techniques to periodic stencils because of the wrap-around dependences in them. To overcome this, we use iteration space folding techniques as a pre-processing stage after which our technique can be applied without any further change.
We have implemented our techniques on top of Pluto-a source-level automatic parallelizer. Experimental evaluation on a 12-core Intel Westmere shows that our code is able to outperform a tuned domain-speciﬁc stencil code generator by 4% to2 x, and previous compiler techniques by a factor of 1.5x to 15x. For the swim benchmark from SPECFP2000, we achieve an .improvement of 5.12 x on a 12-core Intel Westmere and 2.5x on a 16-core AMD Magny-Cours machines, over the auto-parallelizer of Intel C Compiler.2017-05-20T18:30:00Z