相关论文: Deterministic Autopoietic Automata
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
We develop a general model theoretic semantics to rewriting beyond the usual confluence and termination assumptions. This is based on preordered algebra which is a model theory that extends many sorted algebra. In this framework we…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic,…
Let $G$ be a finitely generated group with an automorphism $\varphi\in{\rm Aut}(G)$, or an outer automorphism $\phi\in{\rm Out}(G)$. Suppose that $G$ decomposes into simpler pieces on which the growth behaviour of $\varphi$ and $\phi$ is…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
First, we recount a history of how certain methods using natural self-adjoint operators have, thus far, failed to prove the Riemann Hypothesis. In Section 2, we set the analytical context necessary to have genuine proofs in later sections,…
Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…
Deriving conditional and marginal distributions using conjugacy relationships can be time consuming and error prone. In this paper, we propose a strategy for automating such derivations. Unlike previous systems which focus on relationships…
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal…
We prove a dichotomy between rationality and a natural boundary for the analytic behavior of the Reidemeister zeta function for automorphisms of non-finitely generated torsion abelian groups and for endomorphisms of groups $\mathbb Z_p^d,$…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
Data automata on data words is a decidable model proposed by Boja\'nczyk et al. in 2006. Class automata, introduced recently by Boja\'nczyk and Lasota, is an extension of data automata which unifies different automata models on data words.…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
Deterministic and nondeterministic finite automata with translucent letters were introduced by Nagy and Otto more than a decade ago as Cooperative Distributed systems of a kind of stateless restarting automata with window size one. These…
Coalgebra is a currently quite active field, which aims to look at generic state-based systems (most prominently automata) from a very abstract point of view, mainly using tools from category theory. One of its achievements is to give a…
This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes. It also includes an original algorithm for the intersection of one-way…
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…