• Home
  • Search
  • From Boolean to quantitative notions of correctness
  • Cite Icon5
  • https://doi.org/10.1145/1707801.1706319Copy DOI Icon

From Boolean to quantitative notions of correctness

Show More
  • Abstract
  • Literature Map
  • Citations
  • Similar Papers
Abstract

Classical formalizations of systems and properties are boolean: given a system and a property, the property is either true or false of the system. Correspondingly, classical methods for system analysis determine the truth value of a property, preferably giving a proof if the property is true, and a counterexample if the property is false; classical methods for system synthesis construct a system for which a property is true; classical methods for system transformation, composition, and abstraction aim to preserve the truth of properties. The boolean view is prevalent even if the system, the property, or both refer to numerical quantities, such as the times or probabilities of events. For example, a timed automaton either satisfies or violates a formula of a real-time logic; a stochastic process either satisfies or violates a formula of a probabilistic logic. The classical black-and-white view partitions the world into "correct" and "incorrect" systems, offering few nuances. In reality, of several systems that satisfy a property in the boolean sense, often some are more desirable than others, and of the many systems that violate a property, usually some are less objectionable than others. For instance, among the systems that satisfy the response property that every request be granted, we may prefer systems that grant requests quickly (the quicker, the better), or we may prefer systems that issue few unnecessary grants (the fewer, the better); and among the systems that violate the response property, we may prefer systems that serve many initial requests (the more, the better), or we may prefer systems that serve many requests in the long run (the greater the fraction of served to unserved requests, the better). Formally, while a boolean notion of correctness is given by a preorder on systems and properties, a quantitative notion of correctness is defined by a directed metric on systems and properties, where the distance between a system and a property provides a measure of "fit" or "desirability." There are many ways how such distances can be defined. In a linear-time framework, one assigns numerical values to individual behaviors before assigning values to systems and properties, which are sets of behaviors. For example, the value of a single behavior may be a discounted value, which is largely determined by a prefix of the behavior, e.g., by the number of requests that are granted before the first request that is not granted; or a limit value, which is independent of any finite prefix. A limit value may be an average, such as the average response time over an infinite sequence of requests and grants, or a supremum, such as the worst-case response time. Similarly, the value of a set of behaviors may be an extremum or an average across the values of all behaviors in the set: in this way one can measure the worst of all possible average-case response times, or the average of all possible worst-case response times, etc. Accordingly, the distance between two sets of behaviors may be defined as the worst or average difference between the values of corresponding behaviors. In summary, we propagate replacing boolean specifications for the correctness of systems with quantitative measures for the desirability of systems. In quantitative analysis, the aim is to compute the distance between a system and a property (or between two systems, or two properties); in quantitative synthesis, the objective is to construct a system that has minimal distance from a given property. Multiple quantitative measures can be prioritized (e.g., combined lexicographically into a single measure) or studied along the Pareto curve. Quantitative transformations, compositions, and abstractions of systems are useful if they allow us to bound the induced change in distance from a property. We present some initial results in some of these directions. We also give some potential applications, which not only generalize tradiditional correctness concerns in the functional, timed, and probabilistic domains, but also capture such system measures as resource use, performance, cost, reliability, and robustness.

Similar Papers
  • Research Article
  • Citations1

A New Scheduling Algorithm for Shortening Response Time of Static Priority Task

  • Jun 11, 2022
  • ECTI Transactions on Computer and Information Technology (ECTI-CIT)
  • Takaharu Suzuki +1
  • Conference Article
  • Citations2

An asynchronous data-path design for viterbi decoder

  • Oct 18, 2004
  • Zhao Bing +2
  • Conference Article
  • Citations3

An asynchronous add-compare-select design in CMOS VLSI

  • Jan 01, 2003
  • Zhao Bing +2
  • Research Article
  • Citations17

Response-Time Analysis for Controller Area Networks With Randomly Occurring Messages

  • Apr 01, 2020
  • IEEE Transactions on Vehicular Technology
  • Ryohei Sato +1
  • Conference Article
  • Citations3

Probabilistic worst case response time estimation for multi-core real-time systems

  • Jun 01, 2015
  • Matthias Mucha +2
  • Research Article
  • Citations15

Statistical modeling of emergency medical services’ response and rescue times to road traffic crashes in the Kingdom of Saudi Arabia

  • Nov 14, 2022
  • Case Studies on Transport Policy
  • Ayoub Al-Zabidi +3
  • Research Article

Conditional Dependencies Between Response Time and Item Discrimination: An Item-Level Meta-Analysis.

  • Mar 17, 2026
  • Educational and psychological measurement
  • Joshua B Gilbert +4
  • Conference Article
  • Citations4

A Scratchpad Memory-Based Execution Platform for Functional Reactive Systems and Its Static Timing Analysis

  • Aug 01, 2016
  • Zeinab Kazemi +1
  • Dissertation

Location-Aware Application Deployment in Multi-Cloud

  • Jun 20, 2022
  • Tao Shi
  • Conference Article
  • Citations3

Work in Progress: Response Time Analysis of Real-Time Quantum Computing Systems

  • May 01, 2023
  • Albert M K Cheng
  • Research Article
  • Citations7

The Worst-Case Response Time Analysis for FIFO-based Offset Assigned CAN Messages

  • Jan 01, 2012
  • Journal of Information Processing
  • Yang Chen +3
  • Conference Article

Intelligent Decision-Making Based on Computer Intelligent Algorithms and Big Data Technology

  • Dec 29, 2024
  • Miao Chen
  • Conference Article
  • Citations3

Technique for Detecting Early-Warning Signals of Performance Deterioration in Large Scale Software Systems

  • Apr 17, 2017
  • Raghu Ramakrishnan +1
  • Conference Article
  • Citations12

An EVT-based worst-case Response Time Analysis of complex real-time systems

  • Jan 01, 2013
  • Meng Liu +2
  • Conference Article
  • Citations1

Time analysis for fault-tolerant real-time group-based scheduling

  • Apr 04, 2005
  • Wang Lei +2
Cactus Communications logo

Copyright 2026 Cactus Communications. All rights reserved.