Stories with Tag determinism

• Five Kinds of Nondeterminism

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  Posted: 2025-02-19 20:36:32

  Verbose tl;dr

  Hillel Wayne's post dissects the concept of "nondeterminism" in computer science, arguing that it's often used ambiguously and encompasses five distinct meanings. These are: 1) Implementation-defined behavior, where the language standard allows for varied outcomes. 2) Unspecified behavior, similar to implementation-defined but offering even less predictability. 3) Error/undefined behavior, where anything could happen, often leading to crashes. 4) Heisenbugs, which are bugs whose behavior changes under observation (e.g., debugging). 5) True nondeterminism, exemplified by hardware randomness or concurrency races. The post emphasizes that these are fundamentally different concepts with distinct implications for programmers, and understanding these nuances is crucial for writing robust and predictable software.

  Hillel Wayne's blog post, "Five Kinds of Nondeterminism," delves into the nuanced meanings of "nondeterminism" across different computational contexts, meticulously dissecting the term beyond its common association with randomness. Wayne argues that using the term vaguely can lead to confusion and miscommunication, especially in discussions about security and formal methods. He proposes a typology of five distinct categories of nondeterminism, providing clarity and precision to the concept.

  The first type is implementation-defined nondeterminism. This arises from specifications leaving certain aspects of a system's behavior deliberately unspecified, allowing for variation across different implementations. While the behavior isn't random for a specific implementation, it is unpredictable a priori without knowing the implementation details. Examples include the order of elements returned from a hash table or the specific optimizations a compiler chooses.

  Next, don't care nondeterminism emerges when a specification explicitly allows multiple valid outcomes for a given input, without preference for any specific outcome. The system can choose any of the allowed outcomes, and this choice does not affect the correctness of the system. This is often used in hardware design where certain signal transitions are irrelevant.

  Third, demonic nondeterminism pertains to situations where an adversary or malicious actor can influence the behavior of the system within the constraints of its specification. Formal methods, such as model checking, often utilize this type of nondeterminism to analyze worst-case scenarios and guarantee robustness against adversarial manipulation. A critical example involves assessing the security of a system against various attack vectors.

  The fourth category, probabilistic nondeterminism, is the type most commonly associated with the term "nondeterminism" in everyday usage. Here, system behavior is governed by probabilities, with different outcomes having specific likelihoods. Random number generators and stochastic processes are prime examples of this type. While individual outcomes are unpredictable, the overall distribution of outcomes is often known or can be statistically characterized.

  Finally, scheduler nondeterminism relates specifically to the order of execution in concurrent systems. Multiple processes or threads compete for resources, and the scheduler determines which process gets to execute at a given time. The precise interleaving of execution steps can influence the overall outcome, leading to nondeterministic behavior. This type of nondeterminism poses significant challenges for designing and debugging concurrent systems, necessitating careful synchronization mechanisms to avoid race conditions and other concurrency bugs.

  In conclusion, Wayne emphasizes that understanding these different facets of nondeterminism is essential for clear communication and accurate reasoning about complex systems. He provides concrete examples for each type, illustrating their distinct properties and implications. By disambiguating the term "nondeterminism," Wayne equips readers with a more sophisticated and nuanced understanding of the concept and its various manifestations in different computational domains.

  • nondeterminism
  • programming
  • Computer Science
  • concurrency
  • Parallelism
  • software engineering
  • determinism
  • Multithreading
  • distributed systems
  • randomness
  • Uncertainty
  • Semantics
  • formal methods

  Summary of Comments ( 17 )
  https://news.ycombinator.com/item?id=43107317

  Verbose tl;dr

  Hacker News users discussed various aspects of nondeterminism in the context of Hillel Wayne's article. Several commenters highlighted the distinction between predictable and unpredictable nondeterminism, with some arguing the author's categorization conflated the two. The importance of distinguishing between sources of nondeterminism, such as hardware, OS scheduling, and program logic, was emphasized. One commenter pointed out the difficulty in achieving true determinism even with seemingly simple programs due to factors like garbage collection and just-in-time compilation. The practical challenges of debugging nondeterministic systems were also mentioned, along with the value of tools that can help reproduce and analyze nondeterministic behavior. A few comments delved into specific types of nondeterminism, like data races and the nuances of concurrency, while others questioned the usefulness of the proposed categorization in practice.

  The Hacker News post titled "Five Kinds of Nondeterminism" linking to an article on buttondown.com has generated several comments discussing various aspects of nondeterminism in computer systems.

  Several commenters discuss the nuances and overlaps between the different categories of non-determinism outlined in the article. One commenter points out the difficulty in cleanly separating these categories in practice, arguing that many real-world systems exhibit characteristics of multiple types simultaneously. They use the example of a distributed database, which can have both implementation-defined (order of messages) and essential (concurrent user actions) non-determinism.

  Another commenter focuses on the performance implications of non-determinism, specifically in the context of compiler optimizations. They suggest that eliminating certain kinds of non-determinism can allow for more aggressive optimizations and improved performance predictability.

  The concept of "Heisenbugs" is brought up, with one commenter explaining how these elusive bugs are often a direct consequence of unintended non-determinism. They further link this to the increasing complexity of modern systems and the difficulty in controlling all sources of non-deterministic behavior.

  One commenter delves into the philosophical implications of non-determinism, touching upon the free will vs. determinism debate. They propose that the classification of non-determinism in the article could be applied to this philosophical discussion, offering a new perspective on the nature of choice.

  There's also a discussion about the role of testing and debugging in the presence of non-determinism. One commenter advocates for designing systems that minimize essential non-determinism, arguing that it simplifies testing and makes debugging easier. Another suggests techniques for reproducing and isolating non-deterministic bugs, emphasizing the importance of logging and careful analysis of system behavior.

  A few commenters offer specific examples of non-determinism in different programming languages and systems, illustrating the practical relevance of the article's categorization. They mention issues related to thread scheduling, memory allocation, and network communication, providing concrete examples of how non-determinism manifests in real-world scenarios.

  Finally, some commenters express appreciation for the article's clear explanation of a complex topic, finding the categorization helpful for understanding and addressing non-determinism in their own work. They also suggest potential extensions to the article, such as exploring the relationship between non-determinism and formal verification methods.

• What situations in classical physics are non-deterministic?

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  Posted: 2025-02-15 13:02:46

  Verbose tl;dr

  Classical physics is generally considered deterministic, meaning the future state of a system is entirely determined by its present state. However, certain situations appear non-deterministic due to our practical limitations. These include chaotic systems, where tiny uncertainties in initial conditions are amplified exponentially, making long-term predictions impossible, despite the underlying deterministic nature. Other examples involve systems with a vast number of particles, like gases, where tracking individual particles is infeasible, leading to statistical descriptions and probabilistic predictions, even though the individual particle interactions are deterministic. Finally, systems involving measurement with intrinsic limitations also exhibit apparent non-determinism, arising from our inability to perfectly measure the initial state. Therefore, non-determinism in classical physics is often a result of incomplete knowledge or practical limitations rather than a fundamental property of the theory itself.

  The Stack Exchange post explores the intriguing question of whether determinism, the principle that future states are fully determined by present conditions, truly holds within the realm of classical physics. While classical physics is often presented as a deterministic framework, the discussion reveals several nuanced situations where this deterministic picture may falter or require careful consideration.

  One prominent point of discussion centers around systems with chaotic behavior. In these systems, even minuscule uncertainties or imprecisions in the initial conditions can lead to vastly divergent outcomes over time, making long-term predictions effectively impossible, despite the underlying equations of motion being deterministic. This phenomenon, often illustrated by the butterfly effect, highlights the practical limitations of predictability in deterministic chaotic systems. The post elaborates on how chaotic systems, though deterministic in principle, exhibit a sensitive dependence on initial conditions, leading to practical non-determinism.

  Furthermore, the discussion delves into the role of measurement in classical physics. It raises the question of whether the act of measurement itself introduces an inherent uncertainty, thereby disrupting the deterministic chain of cause and effect. While classical physics generally assumes that measurements can be made with arbitrary precision, in practice, limitations in measurement apparatus and techniques introduce a degree of uncertainty. This inherent uncertainty in measurement, while often negligible, can be a source of apparent non-determinism.

  Another aspect considered is the conceptual challenge posed by systems involving infinite quantities or singularities. For instance, when dealing with phenomena like the collapse of a wave in a perfectly inelastic string or the behavior of particles at singularities, the classical equations of motion may become ill-defined or yield multiple solutions. These situations highlight the potential limitations of classical physics in handling extreme scenarios and can lead to ambiguities that challenge a strictly deterministic interpretation.

  Finally, the concept of thermal equilibrium is examined. While the macroscopic properties of a system in thermal equilibrium appear stable and predictable, the microscopic motion of its constituent particles is inherently random. This statistical nature of thermal equilibrium introduces an element of randomness into the microscopic description, even within the framework of classical physics. Therefore, while the macroscopic behavior appears deterministic, the underlying microscopic dynamics exhibit probabilistic characteristics.

  In summary, the post elucidates several scenarios within classical physics where determinism, while often assumed, can be challenged. These include the practical unpredictability of chaotic systems, the inherent uncertainty associated with measurement, the breakdown of classical descriptions at singularities and infinities, and the statistical nature of microscopic behavior in thermodynamic equilibrium. While the fundamental equations of classical physics are typically deterministic, these nuances demonstrate that determinism in practice can be a complex and sometimes elusive concept.

  • classical physics
  • determinism
  • non-determinism
  • chaos theory
  • statistical mechanics
  • thermodynamics
  • quantum mechanics
  • physics
  • Science

  Summary of Comments ( 66 )
  https://news.ycombinator.com/item?id=43058198

  Verbose tl;dr

  Hacker News users discuss deterministic chaos and how seemingly simple classical systems can exhibit unpredictable behavior due to sensitivity to initial conditions. They mention examples like the double pendulum, dripping faucets, and billiard balls, highlighting how minute changes in starting conditions lead to vastly different outcomes, making long-term prediction impossible. Some argue that while these systems are technically deterministic, the practical limitations of measurement render them effectively non-deterministic. Others point to the three-body problem and the chaotic nature of weather systems as further illustrations. The role of computational limitations in predicting chaotic systems is also discussed, along with the idea that even if the underlying laws are deterministic, emergent complexity can make systems appear unpredictable. Finally, the philosophical implications of determinism are touched upon, with some suggesting that quantum mechanics introduces true randomness into the universe.

  The Hacker News post "What situations in classical physics are non-deterministic?" has generated several comments discussing the concept of determinism in classical physics.

  Some users argue that true non-determinism doesn't exist in classical physics, pointing to chaotic systems as examples of systems that appear random due to our limited computational ability to predict their long-term behavior, but are fundamentally deterministic. They suggest that with sufficient information about initial conditions, one could theoretically predict the future state of a classical system. This includes systems like dice rolls or roulette wheels.

  Others bring up the idea of systems with a "practical" non-determinism, acknowledging that while classical physics may be theoretically deterministic, limitations in measurement and computation often force us to treat certain systems as non-deterministic for practical purposes. This aligns with the concept of chaos mentioned earlier, where even tiny uncertainties in initial measurements can lead to vastly different outcomes, making long-term predictions impossible.

  One user introduces the philosophical implications of determinism and free will, connecting it to the discussion of unpredictability in classical systems. This tangent explores the potential conflict between a deterministic universe and the subjective experience of choice.

  Another point of discussion revolves around the interpretation of statistical mechanics. Some users argue that while individual particles within a gas might follow deterministic Newtonian laws, the vast number of particles makes it practically impossible to track them individually. Therefore, we rely on statistical methods, which introduce probabilistic descriptions and appear non-deterministic. The underlying argument is that this statistical approach is a tool for dealing with complexity, not an indication of true randomness in the system itself.

  Finally, the role of quantum mechanics is briefly touched upon. Some users highlight how the probabilistic nature of quantum mechanics contrasts with the deterministic nature often ascribed to classical physics. However, this comparison isn't a central theme in the discussion.