Hilary Putnam has argued that computational functionalism cannot serve as a foundation for the study of the mind, as every ordinary open physical system implements every finite-state automaton. I argue that Putnam's argument fails, but that it points out the need for a better understanding of the bridge between the theory of computation and the theory of physical systems: the relation of implementation. It also raises questions about the class of automata that can serve as a basis (...) for understanding the mind. I develop an account of implementation, linked to an appropriate class of automata, such that the requirement that a system implement a given automaton places a very strong constraint on the system. This clears the way for computation to play a central role in the analysis of mind. (shrink)

We study the finitely repeated prisoner’s dilemma in which the players are restricted to choosing strategies which are implementable by a machine with a bound on its complexity. One player has to use a finite automaton while the other player has to use a finite perceptron. Some examples illustrate that the sets of strategies which are induced by these two types of machines are different and not ordered by set inclusion. Repeated game payoffs are evaluated according to (...) the limit of means. The main result establishes that a cooperation at almost all stages of the game is an equilibrium outcome if the complexity of the machines the players may use is limited enough and if the length T of the repeated game is sufficiently large. This result persists when more than T states are allowed in the player’s automaton. We further consider a variant of the model in which the two players are restricted to choosing strategies which are implementable by perceptrons and prove that the players can cooperate at most of the stages provided that the complexity of their perceptrons is sufficiently reduced. (shrink)

We show that the fundamental legal structure of a well-written financial contract follows a state-transition logic that can be formalized mathematically as a finite-state machine (specifically, a deterministic finite automaton or DFA). The automaton defines the states that a financial relationship can be in, such as “default,” “delinquency,” “performing,” etc., and it defines an “alphabet” of events that can trigger state transitions, such as “payment arrives,” “due date passes,” etc. The core of a (...) contract describes the rules by which different sequences of events trigger particular sequences of state transitions in the relationship between the counterparties. By conceptualizing and representing the legal structure of a contract in this way, we expose it to a range of powerful tools and results from the theory of computation. These allow, for example, automated reasoning to determine whether a contract is internally coherent and whether it is complete relative to a particular event alphabet. We illustrate the process by representing a simple loan agreement as an automaton. (shrink)

An embedded automaton is introduced to monitor the whole glycolysis process in pancreatic β-cell and it is a hybridization of both non-deterministic finite automaton and push-down automaton. The set of irreversible and reversible reactions in the glycolysis process are related to non-deterministic finite automaton and push-down automaton respectively. The embedded automaton is used to observe the glucose metabolism with the states of acceptance and rejection. The acceptance state of the embedded (...) class='Hi'>automaton depicts the normal level of glycolysis and insulin secretion. The rejection state of this machine shows inhibition of glycolysis which obstructs the secretion of insulin. The subsequent low level of insulin leads to the high blood glucose level also known as hyperglycemia. In this study, the designed machine can be used to regulate the process of glycolysis through a group of regulatory glycolytic enzymes for the treatment of Diabetes mellitus at molecular level. (shrink)

We explore a network architecture introduced by Elman (1988) for predicting successive elements of a sequence. The network uses the pattern of activation over a set of hidden units from time-step 25-1, together with element t, to predict element t + 1. When the network is trained with strings from a particular finite-state grammar, it can learn to be a perfect finite-state recognizer for the grammar. When the network has a minimal number of hidden units, patterns (...) on the hidden units come to correspond to the nodes of the grammar, although this correspondence is not necessary for the network to act as a perfect finite-state recognizer. We explore the conditions under which the network can carry information about distant sequential contingencies across intervening elements. Such information is maintained with relative ease if it is.. (shrink)

Finite-state methods are applied to determine the consequences of events, represented as strings of sets of fluents. Developed to flesh out events used in natural language semantics, the approach supports reasoning about action in AI, including the frame problem and inertia. Representational and inferential aspects of the approach are explored, centering on conciseness of language, context update and constraint application with bias.

Finite-state methods are applied to the Russell-Wiener notion of time (based on events) and developed into an account of interval relations and temporal propositions. Strings are formed and collected in regular languages and regular relations that are argued to embody temporal relations in their various underspecified guises. The regular relations include retractions that reduce computations by projecting strings down to an appropriate level of granularity, and non-deterministic relations defining notions of partiality within and across such levels.

Finite-state descriptions for temporal semantics are outlined through which to distinguish soft inferences reflecting manners of conceptualization from more robust semantic entailments defined over models. Just what descriptions are built (before being interpreted model-theoretically) and how they are grounded in models of reality explain (upon examination) why some inferences are soft.

Finite-state methods are applied to the Russell-Wiener-Kamp notion of time (based on events) and developed into an account of interval relations and semi-intervals. Strings are formed and collected in regular languages and regular relations that are argued to embody temporal relations in their various underspecified guises. The regular relations include retractions that reduce computations by projecting strings down to an appropriate level of granularity, and notions of containment for partiality within and across such levels.

We define a class of finite state automata acting on transfinite sequences, and use these automata to prove that no singular cardinal can be defined by a monadic second order formula over the ordinals.

The argument presented in this paper is not a direct attack or defence of the Chinese Room Argument (CRA), but relates to the premise at its heart, that syntax is not sufficient for semantics, via the closely associated propositions that semantics is not intrinsic to syntax and that syntax is not intrinsic to physics. However, in contrast to the CRA’s critique of the link between syntax and semantics, this paper will explore the associated link between syntax and physics. The main (...) argument presented here is not significantly original – it is a simple reflection upon that originally given by Hilary Putnam (Putnam 1988) and criticised by David Chalmers and others: instead of seeking to justify Putnam’s claim that, “every open system implements every Finite State Automaton (FSA)”, and hence that psychological states of the brain cannot be functional states of a computer, I will seek to establish the weaker result that, over a finite time window every open system implements the trace of a particular FSA Q, as it executes program (p) on input (x). That this result leads to panpsychism is clear as, equating Q (p, x) to a specific Strong AI program that is claimed to instantiate phenomenal states as it executes, and following Putnam’s procedure, identical computational (and ex hypothesi phenomenal) states (ubiquitous little ‘pixies’) can be found in every open physical system. (shrink)

The initial argument presented herein is not significantly original—it is a simple reflection upon a notion of computation originally developed by Putnam and criticised by Chalmers et al. . In what follows, instead of seeking to justify Putnam’s conclusion that every open system implements every Finite State Automaton and hence that psychological states of the brain cannot be functional states of a computer, I will establish the weaker result that, over a finite time window every open (...) system implements the trace of FSA Q, as it executes program on input . If correct the resulting bold philosophical claim is that phenomenal states—such as feelings and visual experiences—can never be understood or explained functionally. (shrink)

Events employed in natural language semantics are characterized in terms of regular languages, each string in which can be regarded as a motion picture. The relevant finite automata then amount to movie cameras/projectors, or more formally, to finite Kripke structures with par- tial valuations. The usual regular constructs (concatena- tion, choice, etc) are supplemented with superposition of strings/automata/languages, realized model-theoretically as conjunction.

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.

This paper presents four state-of-art methods for the finite-state automaton inference based on a sample of labeled strings. The first algorithm is Exbar, and the next three are mathematical models based on ASP, SAT and SMT theories. The potentiality of using multiprocessor computers in the context of automata inference was our research’s primary goal. In a series of experiments, we showed that our parallelization of the exbar algorithm is the best choice when a multiprocessor system is (...) available. Furthermore, we obtained a superlinear speedup for some of the prepared datasets, achieving almost a 5-fold speedup on the median, using 12 and 24 processes. (shrink)

The “surge in use of finite-state methods” ([10]) in computational linguistics has largely, if not completely, left semantics untouched. The present paper is directed towards correcting this situation. Techniques explained in [1] are applied to a fragment of temporal semantics through an approach we call finite-state temporality. This proceeds from the intuition of an event as “a series of snapshots” ([15]; see also [12]), equating snapshots with symbols that collectively form our alphabet. A sequence of snapshots (...) then becomes a string over that alphabet, evoking comic/film strips. Jackendoff has, among others, objected to conceptualizing events in terms of snapshots ([8]). To counter these objections, we step up from events-as-strings to event-typesas-regular languages ([5, 6]), recognizing the need for variable granularity. Beyond the introduction of disjunction implicit in the step from a single string up to a set of strings, we obtain a useful logic from the regular operations and a careful choice of the snapshots (constituting our alphabet). (shrink)

There are currently considerable confusion and disarray about just how we should view computationalism, connectionism and dynamicism as explanatory frameworks in cognitive science. A key source of this ongoing conflict among the central paradigms in cognitive science is an equivocation on the notion of computation simpliciter. ‘Computation’ is construed differently by computationalism, connectionism, dynamicism and computational neuroscience. I claim that these central paradigms, properly understood, can contribute to an integrated cognitive science. Yet, before this claim can be defended, a better (...) understanding of ‘computation’ is required. ‘Digital computation’ is an ambiguous concept. It is not just the classical dichotomy between analogue and digital computation that is the basis for the equivocation on ‘computation’ simpliciter in cognitive science, but also the diversity of extant accounts of digital computation. There are many answers on what it takes for a system to perform digital computation. Answers to this problem range from Turing machine computation, through the formal manipulation of symbols, the execution of algorithms and others, to the strong-pancomputational thesis, according to which every physical system computes every Turing-computable function. Despite some overlap among them, extant accounts of concrete digital computation are non-equivalent, thus, rendering ‘digital computation’ ambiguous. The objective of this dissertation is twofold. First, it is to promote a clearer understanding of concrete digital computation. Accordingly, my main thesis is that not only are extant accounts of concrete digital computation non-equivalent, but most of them are inadequate. I show that these accounts are not just intensionally different (this is quite trivially the case), but also extensionally distinct. In the course of examining several key accounts of concrete digital computation, I propose the instructional information processing account, according to which digital computation is the processing of discrete data in accordance with finite instructional information. The second objective is to establish the foundational role of computation in cognitive science whilst rejecting the purported representational nature of computation. (shrink)

Evans & Levinson's (E&L's) major point is that human languages are intriguingly diverse rather than (like animal communication systems) uniform within the species. This does not establish a about language universals, or advance the ill-framed pseudo-debate over universal grammar. The target article does, however, repeat a troublesome myth about Fitch and Hauser's (2004) work on pattern learning in cotton-top tamarins.

This paper considers the existence of finite equational axiomatisations of behavioural equivalences over a calculus of finite state processes. To express even simple properties such as μxE = μxE[E/x] some notation for substitutions is required. Accordingly, the calculus is embedded in a simply typed lambda calculus, allowing such schemas to be expressed as equations between terms containing first order variables. A notion of first order trace congruence over such terms is introduced and used to show that no (...) finite set of such equations is sound and complete for any reasonable equivalence finer than trace equivalence. The intermediate results are then applied to give two nonaxiomatisability results over calculi of regular expressions. (shrink)

In the first part of this paper, two arguments, one by Chomsky, and one by Bar-Hillel and Shamir, are examined in detail and rejected. Both arguments purport to show that the structure of English precludes its having a finite state grammar which correctly enumerates just the well formed sentences of English. In the latter part of the paper I consider the problem of supporting claims about the structure and properties of a natural language when no grammar for the (...) language has yet been accepted. (shrink)

Reichenbach's event, reference and speech times are interpreted semantically by stringing and superposing sets of temporal formulae, structured within regular languages. Notions of continuation branches and of inertia, bound (in a precise sense) by reference time, are developed and applied to the progressive and the perfect.

This paper proposes an innovative approach to achieving real-time polymorphic behavior detection, and its direct application to blockchain-focused smart-contracts. We devise a method based on a non-deterministic finite state machine to perform approximate pattern-matching, using a look-ahead mechanism implemented through a concept similar to that of a sliding window, and using threshold-based similarity checking at every state in the automaton. We introduce and formalize our approach, discuss the challenges we faced and then test it in a (...) real-world environment. The experimental results obtained showed a significant speed-up of our approach, as compared to the classic similarity measures used commonly in such scenarios. (shrink)

For each class in the piecewise-local subregular hierarchy, a relativized (tier-based) variant is defined. Algebraic as well as automata-, language-, and model-theoretic characterizations are provided for each of these relativized classes, except in cases where this is provably impossible. These various characterizations are necessarily intertwined due to the well-studied logic-automaton connection and the relationship between finite-state automata and (syntactic) semigroups. Closure properties of each class are demonstrated by using automata-theoretic methods to provide constructive proofs for the closures (...) that do hold and giving language-theoretic counterexamples for those that do not. The net result of all of this is that, rather than merely existing as an operationally-defined parallel set of classes, these relativized variants integrate cleanly with the other members of the piecewise-local subregular hierarchy from every perspective. Relativization may even prove useful in the characterization of star-free, as every star-free stringset is the preprojection of another (also star-free) stringset whose syntactic semigroup is not a monoid. (shrink)

The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by (...) time-varying state delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method. (shrink)

For any unit vector in an inner product space S, we define a mapping on the system of all ⊥-closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate (...) systems of subspaces. Finally, the result will be generalized to general inner product spaces. (shrink)

European Journal of Philosophy, EarlyView.

European Journal of Philosophy, Volume 30, Issue 3, Page 943-960, September 2022.

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular (...) class='Hi'>Automaton method to solve the PDEs. We submit wholeheartedly Robert Kurucz’s hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details. (shrink)

Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/ extrinsic perception . These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, consequently, a discrete model of Heisenberg uncertainty has been suggested. For this aim the classical theory of finite automata — which considers automata with initial states — (...) is not adequate, and a new approach is necessary. A study of finite deterministic automata without initial states is exactly the aim of this paper. We will define and investigate the complexity of various types of simulations between automata. Minimal automata will be constructed and proven to be unique up to an isomorphism. We will build our results on an extension of Myhill-Nerode technique; all constructions will make use of “automata responses” to simple experiments only, i.e., no information about the internal machinery will be considered available. (shrink)

I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite frequentism, in which Gibbs’ concept of an infinite ensemble of gases is replaced by the quantum state expressed as a superposition of a finite number of decohering microstates. It is a form of finite and actual frequentism (...) (as opposed to hypothetical frequentism) insofar as all the microstates exist, in keeping with the decoherence-based Everett interpretation, and some versions of pilot-wave theory. (shrink)

Solid-state processing of metal material is a very complex physical and chemical process, which is coupled by a series of variations including heat transfer, momentum transfer, mass transfer, and phase change. Applying three-dimensional finite element numerical method to the simulation of solid-state processing can perform analysis of metal material’s forging processes before production trial production, can obtain their relevant information such as material flow law, temperature field, and strain field under the minimum physical test conditions, thereby predicting (...) metal material’s forming defects and improving their forging quality. On the basis of summarizing and analyzing previous research works, this paper expounded the current status and significance of solid-state processing of metal materials, elaborated the development background, current status, and future challenges of 3D finite element numerical simulation, introduced the discrimination method and free surface solution method of numerical simulation calculation, conducted finite element model’s geometric assumptions, material selection, element division, model establishment, parameter selection, and initial and boundary condition determination, and simulated and analyzed rheological casting, remelting heating, thixoforming, and rotary piercing processes of metal materials. The results show that the 3D finite element numerical method can not only simulate various processes of flow field, temperature field, stress field, and microstructure in solid-state processing but also can provide a reliable basis for effectively obtaining a reasonable description and finding a more optimized design plan for metal material processing in a short time, which plays an important role in understanding and analyzing solid metal forming process, controlling and optimizing process parameters, guiding and mastering rheological casting, and secondary heating and rotary piercing of metal materials. (shrink)

It will be settled out for the open problem of designing an r-order finite-time state observer for reaction-diffusion genetic regulatory networks with time-varying delays. By assuming the Dirichlet boundary conditions, aiming to estimate the mRNA and protein concentrations via available network measurements. Firstly, sufficient F-T stability conditions for the filtering error system have been investigated via constructing an appropriate Lyapunov–Krasovskii functional and using several integral inequalities and convex technique simultaneously. These conditions are delay-dependent and reaction-diffusion-dependent and can be (...) checked by MATLAB toolbox. Furthermore, a method is proposed to design an r-order F-T state observer, and the explicit expressions of observer gains are given. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method. (shrink)