Related papers: An Algebraic Approach for Reasoning About Informat…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
Performance analysis is challenging as different components (e.g.,different libraries, and applications) of a complex system can interact with each other. However, few existing tools focus on understanding such interactions. To bridge this…
Availability is crucial to the security of distributed systems, but guaranteeing availability is hard, especially when participants in the system may act maliciously. Quorum replication protocols provide both integrity and availability:…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
Many tool-based Retrieval Augmented Generation (RAG) systems lack precise mechanisms for tracing final responses back to specific tool components -- a critical gap as systems scale to complex multi-agent architectures. We present…
In this paper we propose a novel index to quantify and measure the flow of information on macro and micro scales. We discuss the implications of this index for knowledge management fields and also as intellectual capital that can thus be…
We present a framework for quantifying information flow within general quantum processes. For this purpose, we introduce the signaling power of quantum channels and discuss its relevant operational properties. This function supports…
Quantum cryptography has been extensively studied in the last twenty years, but information-flow security of quantum computing and communication systems has been almost untouched in the previous research. Duo to the essential difference…
Quantitative program analysis involves computing numerical quantities about individual or collections of program executions. An example of such a computation is quantitative information flow analysis, where one estimates the amount of…
Complex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and…
Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time noisy algorithms, a prominent analysis technique relies on…
We develop an algebraic theory of synchronous dataflow networks. First, a basic algebraic theory of networks, called BNA (Basic Network Algebra), is introduced. This theory captures the basic algebraic properties of networks. For…
What is the minimal algebraic structure to reason about information flow? Do we really need the full power of Boolean algebras with co-closure and de Morgan dual operators? How much can we weaken and still be able to reason about…
This paper considers the problem of resource allocation in stream processing, where continuous data flows must be processed in real time in a large distributed system. To maximize system throughput, the resource allocation strategy that…
Explainable systems expose information about why certain observed effects are happening to the agents interacting with them. We argue that this constitutes a positive flow of information that needs to be specified, verified, and balanced…
This work proposes an algebraic model for classical information theory. We first give an algebraic model of probability theory. Information theoretic constructs are based on this model. In addition to theoretical insights provided by our…
Understanding how data moves, transforms, and persists, known as data flow, is fundamental to reasoning in procedural tasks. Despite their fluency in natural and programming languages, large language models (LLMs), although increasingly…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
Based on our previous work on truly concurrent process algebras APTC, we use it to verify the security protocols. This work (called Secure APTC, abbreviated SAPTC) have the following advantages in verifying security protocols: (1) It has a…
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