相关论文: Conway's cosmological theorem and automata theory

Ramsey's theorem asserts that every $k$-coloring of $[\omega]^n$ admits an infinite monochromatic set. Whenever $n \geq 3$, there exists a computable $k$-coloring of $[\omega]^n$ whose solutions compute the halting set. On the other hand,…

We introduce the abstract notions of "monadic operational semantics", a small-step semantics where computational effects are modularly modeled by a monad, and "type-and-effect system", including "effect types" whose interpretation lifts…

A new hidden variable theory is proposed, according to which particles follows definite trajectories, as in Bohmian Mechanics or Nelson's stochastic mechanics; in the new theory, however, the trajectories are classical, i.e. Newtonian. This…

Argument mining is to analyze argument structure and extract important argument information from unstructured text. An argument mining system can help people automatically gain causal and logical information behind the text. As…

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…

We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

We introduce an original model of quantum phenomena, a model that provides a picture of a "deep structure", an "underlying pattern" of quantum dynamics. We propose that the source of a particle and all of that particle's possible detectors…

Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic…

We analyze the pointwise convergence of a sequence of computable elements of L^1(2^omega) in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA_0,…

We show that there exists a one-to-one correspondence between the set of number-conserving cellular automata (CA) with $q$ inputs and the set of balanced sequences with $q$ terms. This allows to enumerate number-conserving CA. We also show…

A word $w$ of letters on edges of underlying graph $\Gamma$ of deterministic finite automaton (DFA) is called synchronizing if $w$ sends all states of the automaton to a unique state. J. \v{C}erny discovered in 1964 a sequence of $n$-state…

The basic hypothesis of a post-Copernican Cosmological theory is that {\em all the points} of the Universe have to be essentially equivalent: this hypothesis is required in order to avoid any privileged {\em observer}. This assumption has…

This paper links prosody to the information in a text and how it is processed by the speaker. It describes the operation and output of LOQ, a text-to-speech implementation that includes a model of limited attention and working memory.…

Conway and Kochen have presented a "free will theorem" (Notices of the AMS 56, pgs. 226-232 (2009)) which they claim shows that "if indeed we humans have free will, then [so do] elementary particles." In a more precise fashion, they claim…

This paper develops an assume-guarantee (AG) framework for the compositional verification of probabilistic automata (PAs) with uncertain transition probabilities. We study parametric probabilistic automata (pPAs), where probabilities are…

The Cosmic Defect theory has been confronted with four observational constraints: primordial nuclear species abundances emerging from the big bang nucleosynthesis; large scale structure formation in the universe; cosmic microwave background…

We construct a cosmological toy model in which a step-function ``cosmological constant'' is taken into consideration beside ordinary matter. We assume that $\Lambda$ takes two values depending on the epoch, and matter goes from a radiation…

We present five results in the theory of structural governance for cognitive workflow systems. Three are mechanized in Coq 8.19 using the Interaction Trees library with parameterized coinduction; two are proved on paper with explicit…

This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…