136 research outputs found
Global semantic typing for inductive and coinductive computing
Inductive and coinductive types are commonly construed as ontological
(Church-style) types, denoting canonical data-sets such as natural numbers,
lists, and streams. For various purposes, notably the study of programs in the
context of global semantics, it is preferable to think of types as semantical
properties (Curry-style). Intrinsic theories were introduced in the late 1990s
to provide a purely logical framework for reasoning about programs and their
semantic types. We extend them here to data given by any combination of
inductive and coinductive definitions. This approach is of interest because it
fits tightly with syntactic, semantic, and proof theoretic fundamentals of
formal logic, with potential applications in implicit computational complexity
as well as extraction of programs from proofs. We prove a Canonicity Theorem,
showing that the global definition of program typing, via the usual (Tarskian)
semantics of first-order logic, agrees with their operational semantics in the
intended model. Finally, we show that every intrinsic theory is interpretable
in a conservative extension of first-order arithmetic. This means that
quantification over infinite data objects does not lead, on its own, to
proof-theoretic strength beyond that of Peano Arithmetic. Intrinsic theories
are perfectly amenable to formulas-as-types Curry-Howard morphisms, and were
used to characterize major computational complexity classes Their extensions
described here have similar potential which has already been applied
Formal Theories for Linear Algebra
We introduce two-sorted theories in the style of [CN10] for the complexity
classes \oplusL and DET, whose complete problems include determinants over Z2
and Z, respectively. We then describe interpretations of Soltys' linear algebra
theory LAp over arbitrary integral domains, into each of our new theories. The
result shows equivalences of standard theorems of linear algebra over Z2 and Z
can be proved in the corresponding theory, but leaves open the interesting
question of whether the theorems themselves can be proved.Comment: This is a revised journal version of the paper "Formal Theories for
Linear Algebra" (Computer Science Logic) for the journal Logical Methods in
Computer Scienc
Conceptual Modeling of a Quantum Key Distribution Simulation Framework Using the Discrete Event System Specification
Quantum Key Distribution (QKD) is a revolutionary security technology that exploits the laws of quantum mechanics to achieve information-theoretical secure key exchange. QKD is suitable for use in applications that require high security such as those found in certain commercial, governmental, and military domains. As QKD is a new technology, there is a need to develop a robust quantum communication modeling and simulation framework to support the analysis of QKD systems. This dissertation presents conceptual modeling QKD system components using the Discrete Event System Specification (DEVS) formalism to assure the component models are provably composable and exhibit temporal behavior independent of the simulation environment. These attributes enable users to assemble and simulate any collection of compatible components to represent QKD system architectures. The developed models demonstrate closure under coupling and exhibit behavior suitable for the intended analytic purpose, thus improving the validity of the simulation. This research contributes to the validity of the QKD simulation, increasing developer and user confidence in the correctness of the models and providing a composable, canonical basis for performance analysis efforts. The research supports the efficient modeling, simulation, and analysis of QKD systems when evaluating existing systems or developing next generation QKD cryptographic systems
Mobile Resource Guarantees for Smart Devices
Abstract. We present the Mobile Resource Guarantees framework: a system for ensuring that downloaded programs are free from run-time violations of resource bounds. Certificates are attached to code in the form of efficiently checkable proofs of resource bounds; in contrast to cryptographic certificates of code origin, these are independent of trust networks. A novel programming language with resource constraints encoded in function types is used to streamline the generation of proofs of resource usage.
Patterns and Rewrite Rules for Systematic Code Generation (From High-Level Functional Patterns to High-Performance OpenCL Code)
Computing systems have become increasingly complex with the emergence of
heterogeneous hardware combining multicore CPUs and GPUs. These parallel
systems exhibit tremendous computational power at the cost of increased
programming effort. This results in a tension between achieving performance and
code portability. Code is either tuned using device-specific optimizations to
achieve maximum performance or is written in a high-level language to achieve
portability at the expense of performance.
We propose a novel approach that offers high-level programming, code
portability and high-performance. It is based on algorithmic pattern
composition coupled with a powerful, yet simple, set of rewrite rules. This
enables systematic transformation and optimization of a high-level program into
a low-level hardware specific representation which leads to high performance
code.
We test our design in practice by describing a subset of the OpenCL
programming model with low-level patterns and by implementing a compiler which
generates high performance OpenCL code. Our experiments show that we can
systematically derive high-performance device-specific implementations from
simple high-level algorithmic expressions. The performance of the generated
OpenCL code is on par with highly tuned implementations for multicore CPUs and
GPUs written by expertsComment: Technical Repor
Reasoning About Vote Counting Schemes Using Light-weight and Heavy-weight Methods
We compare and contrast our experiences in specifying, implementing
and verifying the monotonicity property of a simple plurality voting
scheme using modern light-weight and heavy-weight verification tools
Unbiased Watermark for Large Language Models
The recent advancements in large language models (LLMs) have sparked a
growing apprehension regarding the potential misuse. One approach to mitigating
this risk is to incorporate watermarking techniques into LLMs, allowing for the
tracking and attribution of model outputs. This study examines a crucial aspect
of watermarking: how significantly watermarks impact the quality of
model-generated outputs. Previous studies have suggested a trade-off between
watermark strength and output quality. However, our research demonstrates that
it is possible to integrate watermarks without affecting the output probability
distribution with appropriate implementation. We refer to this type of
watermark as an unbiased watermark. This has significant implications for the
use of LLMs, as it becomes impossible for users to discern whether a service
provider has incorporated watermarks or not. Furthermore, the presence of
watermarks does not compromise the performance of the model in downstream
tasks, ensuring that the overall utility of the language model is preserved.
Our findings contribute to the ongoing discussion around responsible AI
development, suggesting that unbiased watermarks can serve as an effective
means of tracking and attributing model outputs without sacrificing output
quality
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