Mathematical Logic: Proof Theory, Constructive Mathematics

[no abstract available

Parameter Synthesis for Markov Models

Markov chain analysis is a key technique in reliability engineering. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not---or only partially---known. This motivates considering parametric models with transitions labeled with functions over parameters. Whereas traditional Markov chain analysis evaluates a reliability metric for a single, fixed set of probabilities, analysing parametric Markov models focuses on synthesising parameter values that establish a given reliability or performance specification $\varphi$. Examples are: what component failure rates ensure the probability of a system breakdown to be below 0.00000001?, or which failure rates maximise reliability? This paper presents various analysis algorithms for parametric Markov chains and Markov decision processes. We focus on three problems: (a) do all parameter values within a given region satisfy $\varphi$?, (b) which regions satisfy $\varphi$ and which ones do not?, and (c) an approximate version of (b) focusing on covering a large fraction of all possible parameter values. We give a detailed account of the various algorithms, present a software tool realising these techniques, and report on an extensive experimental evaluation on benchmarks that span a wide range of applications.Comment: 38 page

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Runtime Systems for Persistent Memories

Emerging persistent memory (PM) technologies promise the performance of DRAM with the durability of disk. However, several challenges remain in existing hardware, programming, and software systems that inhibit wide-scale PM adoption. This thesis focuses on building efficient mechanisms that span hardware and operating systems, and programming languages for integrating PMs in future systems. First, this thesis proposes a mechanism to solve low-endurance problem in PMs. PMs suffer from limited write endurance---PM cells can be written only 10^7-10^9 times before they wear out. Without any wear management, PM lifetime might be as low as 1.1 months. This thesis presents Kevlar, an OS-based wear-management technique for PM, that requires no new hardware. Kevlar uses existing virtual memory mechanisms to remap pages, enabling it to perform both wear leveling---shuffling pages in PM to even wear; and wear reduction---transparently migrating heavily written pages to DRAM. Crucially, Kevlar avoids the need for hardware support to track wear at fine grain. It relies on a novel wear-estimation technique that builds upon Intel's Precise Event Based Sampling to approximately track processor cache contents via a software-maintained Bloom filter and estimate write-back rates at fine grain. Second, this thesis proposes a persistency model for high-level languages to enable integration of PMs in to future programming systems. Prior works extend language memory models with a persistency model prescribing semantics for updates to PM. These approaches require high-overhead mechanisms, are restricted to certain synchronization constructs, provide incomplete semantics, and/or may recover to state that cannot arise in fault-free program execution. This thesis argues for persistency semantics that guarantee failure atomicity of synchronization-free regions (SFRs) --- program regions delimited by synchronization operations. The proposed approach provides clear semantics for the PM state that recovery code may observe and extends C++11's "sequential consistency for data-race-free" guarantee to post-failure recovery code. To this end, this thesis investigates two designs for failure-atomic SFRs that vary in performance and the degree to which commit of persistent state may lag execution. Finally, this thesis proposes StrandWeaver, a hardware persistency model that minimally constrains ordering on PM operations. Several language-level persistency models have emerged recently to aid programming recoverable data structures in PM. The language-level persistency models are built upon hardware primitives that impose stricter ordering constraints on PM operations than the persistency models require. StrandWeaver manages PM order within a strand, a logically independent sequence of PM operations within a thread. PM operations that lie on separate strands are unordered and may drain concurrently to PM. StrandWeaver implements primitives under strand persistency to allow programmers to improve concurrency and relax ordering constraints on updates as they drain to PM. Furthermore, StrandWeaver proposes mechanisms that map persistency semantics in high-level language persistency models to the primitives implemented by StrandWeaver.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155100/1/vgogte_1.pd