Showing papers on "Continuous automaton published in 2022"
TL;DR: The analysis of properties of the cellular automata class introduced by the authors, including the average velocity of a cellular automaton, which characterizes the average intensity of changes in the states of the automaton’s cells for a given initial state, is developed.
Abstract: This paper develops the analysis of properties of the cellular automata class introduced by the authors. It is assumed that the set of automaton cells is finite and forms a closed lattice, and there are two states for each automaton cell. We consider a new concept. This concept is the average velocity of a cellular automaton, which characterizes the average intensity of changes in the states of the automaton’s cells for a given initial state. The automaton velocity is equal to 1 if the state of any cell changes at each step. The spectrum of average velocities of a cellular automaton is the set of average velocities for different initial states. Since the state space is finite, the automaton, starting from a certain moment of time, is in periodically repeating states of a cycle, and thus, the research of the velocity spectrum is related to the problem of studying the set of the automaton cycles. For elementary cellular automata, the introduced class consists of a subclass of automata such that the conjugation trasformation of an automaton is the automaton itself (Subclass A) or the reflection of the automaton (Subclass B). For this class, it is proved that the spectrum of the automaton contains the value v0 if and only if the spectrum of the complementary automaton contains the value 1−v0 (the sum of the index of elementary cellular automaton and the complementary automaton is 255). For automata of Subclasses A and B, the set of cycles and the velocity spectrum are studied. For Subclass A, a theorem has been proved such that in accordance with this theorem, if two automata complementary to each other start evolving in the same initial state, then the sum of their average velocities is equal to 1. This theorem for Subclass A is generalized to cellular automata, invariant under the conjugation transformation, of more general type than elementary automata. Generalizations of the theorem have been given for the class of one-dimensional cellular automata with a neighborhood containing 2r+1 cells (the next state of the cell depends on the present states of this cell, r cells on the left and r cells on the right) and for some traditionally considered classes of two-dimensional automata. Some elementary cellular automata belonging to the class considered in the paper can be interpreted as transport models. The properties of the spectra for these automata are studied and compared with the properties of elementary cellular automata not invariant under the considered transformations and can also be interpreted as transport models. The analytical results obtained for these simple models can be used to study the qualitative properties and limiting behavior of more complex transport models.
1 citations
TL;DR: In this paper , the problem of low-power assignment of the partial states of a parallel automaton is considered and a method to solve that problem is suggested that provides minimizing the number of memory elements in the implementing circuit of the automaton and minimization of their switching activity.
Abstract: The problem of a low-power assignment of the partial states of a parallel automaton is considered. A method to solve that problem is suggested that provides minimizing the number of memory elements in the implementing circuit of the automaton and minimization of their switching activity. The problem is reduced to finding a minimal weighted cover of a graph with its complete bipartite sub-graphs (bi-cliques).
1 citations
TL;DR: In this article , the orbits of automaton semigroups and groups were investigated for general automata and groups, both for general and for some special subclasses, and it was shown that the finiteness problem for automaton groups is undecidable.
Abstract: We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we show that a more general version of the finiteness problem for automaton groups is undecidable. This problem is equivalent to the finiteness problem for left principal ideals in automaton semigroups generated by complete and reversible automata. Then, we look at w-word (i.\,e.\ right infinite words) with a finite orbit. We show that every automaton yielding an w-word with a finite orbit already yields an ultimately periodic one, which is not periodic in general, however. On the algorithmic side, we observe that it is not possible to decide whether a given periodic w-word has an infinite orbit and that we cannot check whether a given reversible and complete automaton admits an w-word with a finite orbit, a reciprocal problem to the finiteness problem for automaton semigroups in the reversible case. Finally, we look at automaton groups generated by reversible but not bi-reversible automata and show that many words have infinite orbits under the action of such automata.
TL;DR: There is a weakly-universal 5-state RNCA, i.e., it is possible to simulate any combinational logic circuit, and a configuration which simulates the rule 110 cellular automaton is shown.
TL;DR: Group cellular automata generalize the concept of additive automata into non-commutative groups as mentioned in this paper , and the set of space-time diagrams of a group cellular automaton is a group shift.
Abstract: We consider subshifts and cellular automata in the setup where the state set is a finite group. The group does not need to be commutative. A subshift that is also a subgroup is called a group shift, and we call a cellular automaton on a group shift a group cellular automaton if it is also a group homomorphism. Group cellular automata generalize the much studied concept of additive cellular automata into non-commutative groups. The set of space-time diagrams of a group cellular automaton is a group shift, so we can apply classical results by Bruce Kitchens and Klaus Schmidt on group shifts to analyze group cellular automata. In particular, we can effectively construct the limit set and the trace subshifts of any group cellular automaton. We can then algorithmically decide many properties concerning the cellular automaton that are in general undecidable. The talk is based on a joint work with Pierre Béaur.KeywordsGroup cellular automataGroup shiftsSymbolic dynamicsDecidability
15 Apr 2022
TL;DR: In this article , a cellular-automaton based, two-dimensional (2D) lattice model which generates global oscillations in the EEG spectrum as well as time series of local field potentials resembling those observed during slow wave sleep is described.
Abstract: We describe a cellular-automaton based, two-dimensional (2D) lattice model which generates global oscillations in the EEG spectrum as well as time series of local field potentials resembling those observed during slow wave sleep. This is made possible by the presence of pacemakers (local oscillators) which can be spontaneously ignited and whose activity propagates through space to synchronize all connected nodes.
TL;DR: It is shown that by varying the initial state of the cellular automaton and the structure of feedbacks as control tools, it seems possible to form binary pseudo-random streams of states with different structures, different order of flow elements, bringing their characteristics closer to random ones.
Abstract: Objective. Development of a method for organizing the process of forming flows register structure, patented by the author at the Department of DSTU, which is a cellular automaton of binary sequences with a controlled structure of "cellular" automata in homogeneous register environments. Method. To solve the set system problem, a process model was built in order to determine the factors that allow changing the sequence of flow elements. Result. When studying the most common generators of pseudo-random streams based on linear register media with modulo two adders in feedback circuits, which are "cellular" automata, it was established from the tables of environment states that the factors determining the structure of the generated streams of binary sequences are the sequence of states , are the initial state of the register of a homogeneous medium and the feedback structure determined by the transition function of the cellular automaton. Conclusion. It is shown that by varying the initial state of the cellular automaton and the structure of feedbacks as control tools, it seems possible to form binary pseudo-random streams of states with different structures, different order of flow elements, bringing their characteristics closer to random ones. Examples of the implementation of the flow structure control process are given, confirming this assumption. A typical structure of a stream shaper with a managed structure based on a homogeneous one is given.
30 Mar 2022
TL;DR: In this paper , the authors proposed a probabilistically-switch-action-on-failure learning automaton (PSAFA), which can switch from a present state in any chain to the initial state of the next chain in the circle with some finite probability.
Abstract: <p>We present the novel concept of Probabilistically-Switch-Action-on-Failure learning automaton (PSAFA). The PSAFA is a fixed structure stochastic automaton (FSSA), characterized by a fan-shaped state transition diagram where each branch of the state space is a chain of D states, and is associated with a particular action. The first states of all chains form a circle of initial states. The PSAFA can switch from a present state in any chain to the initial state of the next chain in the circle, on each failure, with some finite probability. This probability, which plays the role of an action- switching probability, is a function of the distance of the present state from initial state of its branch. The learning behavior of PSAFA is determined by the dependence of the action switching probability on the distance from the initial state.</p><p>The probabilistic action-switching capability distinguishes PSAFA from conventional FSSA that have deterministic action selection at each state, and only some states transit to states with a different Probabilistically-switch-action-on-failure Automaton action. This action-switching capability at any time is also typical for conventional variable structure stochastic automata (VSSA) but it comes with added computational complexity. VSSA are more adaptive than FSSA in non-stationary environments because of this action-switching capability. We believe that the addition of this capability should also make the PSAFA more adaptive in non-stationary environments than classical FSSA while preserving the simplified computational complexity of FSSA.</p><p>The effectiveness of the proposed framework is demonstrated through the theoretical analysis of optimality of the PSAF learning automaton in stationary environments in part 1 of this 2-part paper.</p><div><br></div>
28 Mar 2022
TL;DR: In this article , a cellular-automaton based, two-dimensional (2D) lattice model which generates global oscillations in the EEG spectrum as well as time series of local field potentials resembling those observed during slow wave sleep is described.
Abstract: We describe a cellular-automaton based, two-dimensional (2D) lattice model which generates global oscillations in the EEG spectrum as well as time series of local field potentials resembling those observed during slow wave sleep. This is made possible by the presence of pacemakers (local oscillators) which can be spontaneously ignited and whose activity propagates through space to synchronize all connected nodes.
30 Mar 2022
TL;DR: In this article , simulations of Probabilistically-Switch-Action-on-Failure learning automaton (PSAFA) are presented in various stationary and non-stationary environments.
Abstract: <div> <div> <div> <p>In this part of the two-part paper, simulations of Probabilistically-Switch-Action-on-Failure learning automaton (PSAFA) are presented in various stationary and non-stationary environments. The PSAFA is a novel fixed structure stochastic automaton (FSSA) framework, and its analytical model is presented in detail in Part 1 of this paper set. The key differentiating feature of this automaton is that it allows action switching in every state. We anticipate that this feature attributes PSAFA dynamic properties that make certain aspects of its performance superior to other FSSA that do not possess this property.</p> <p>In this paper, simulations of the PSAFA in comparison with other FSSA are considered in two types of environments: a stationary environment (with fixed penalty probabilities) and a non-stationary environment, where the penalty probabilities are changing in time periodically as a sinusoidal function. In both cases the simulation demonstrates a dramatic difference in performance for these types of learning automata. The PSAFA shows its huge advantage in adaptability that leads to a better performance for the length of the simulation up to 30,000-150,000 steps. Only for very long stationary conditions Tsetlin automata outperforms PSAFA. In the case of sinusoidal modulations, the PSAFA tremendously outperforms other types of FSSA for all modulation frequencies and for all depths D>3. The performance of PSAFA does not deteriorate with increasing modulation frequency, while other FSSA are not resilient to that increase. </p> </div> </div> </div>
30 Mar 2022
TL;DR: In this article , the authors proposed a probabilistically-switch-action-on-failure learning automaton (PSAFA), which can switch from a present state in any chain to the initial state of the next chain in the circle with some finite probability.
Abstract: <p>We present the novel concept of Probabilistically-Switch-Action-on-Failure learning automaton (PSAFA). The PSAFA is a fixed structure stochastic automaton (FSSA), characterized by a fan-shaped state transition diagram where each branch of the state space is a chain of D states, and is associated with a particular action. The first states of all chains form a circle of initial states. The PSAFA can switch from a present state in any chain to the initial state of the next chain in the circle, on each failure, with some finite probability. This probability, which plays the role of an action- switching probability, is a function of the distance of the present state from initial state of its branch. The learning behavior of PSAFA is determined by the dependence of the action switching probability on the distance from the initial state.</p><p>The probabilistic action-switching capability distinguishes PSAFA from conventional FSSA that have deterministic action selection at each state, and only some states transit to states with a different Probabilistically-switch-action-on-failure Automaton action. This action-switching capability at any time is also typical for conventional variable structure stochastic automata (VSSA) but it comes with added computational complexity. VSSA are more adaptive than FSSA in non-stationary environments because of this action-switching capability. We believe that the addition of this capability should also make the PSAFA more adaptive in non-stationary environments than classical FSSA while preserving the simplified computational complexity of FSSA.</p><p>The effectiveness of the proposed framework is demonstrated through the theoretical analysis of optimality of the PSAF learning automaton in stationary environments in part 1 of this 2-part paper.</p><div><br></div>
TL;DR: In this paper , the authors introduced virtual cyclic cellular automata and showed that the inverse of a reversible (2R+1)-cyclic automaton with periodic boundary conditions is an invariant dipolynomial.
TL;DR: In this paper , it was shown that the deterministic membership problem for register automata is decidable when the input automaton is a nondeterministic one-register automaton (possibly with epsilon transitions) and the number of registers of the output deterministic register automaton was fixed.
Abstract: The deterministic membership problem for timed automata asks whether the timed language given by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. An analogous problem can be stated in the setting of register automata. We draw the complete decidability/complexity landscape of the deterministic membership problem, in the setting of both register and timed automata. For register automata, we prove that the deterministic membership problem is decidable when the input automaton is a nondeterministic one-register automaton (possibly with epsilon transitions) and the number of registers of the output deterministic register automaton is fixed. This is optimal: We show that in all the other cases the problem is undecidable, i.e., when either (1) the input nondeterministic automaton has two registers or more (even without epsilon transitions), or (2) it uses guessing, or (3) the number of registers of the output deterministic automaton is not fixed. The landscape for timed automata follows a similar pattern. We show that the problem is decidable when the input automaton is a one-clock nondeterministic timed automaton without epsilon transitions and the number of clocks of the output deterministic timed automaton is fixed. Again, this is optimal: We show that the problem in all the other cases is undecidable, i.e., when either (1) the input nondeterministic timed automaton has two clocks or more, or (2) it uses epsilon transitions, or (3) the number of clocks of the output deterministic automaton is not fixed.
23 Dec 2022
TL;DR: In this paper , a fuzzy cellular automaton obtained from an elementary cellular automata of rule number 38 is investigated, and its asymptotic solutions are classified into two types.
Abstract: Fuzzy cellular automaton is a dynamical system with a continuous state value embedding a cellular automaton with a discrete state value. We investigate a fuzzy cellular automaton obtained from an elementary cellular automaton of rule number 38. Its asymptotic solutions are classified into two types. One is a solution where stable propagating waves exist, and the other is a static uniform solution of constant value.
TL;DR: In this paper , the authors consider the problem of self-stabilizing cellular automata under a finite set of local constraints, where the automaton must eventually fall back into the space of valid configurations where it remains still.
Abstract: Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a valid configuration, the cellular automaton must eventually fall back into the space of valid configurations where it remains still. We allow the cellular automaton to use extra symbols, but in that case, the extra symbols can also appear in the initial finite perturbation. For several classes of local constraints (e.g., $k$-colourings with $k
eq 3$, and North-East deterministic constraints), we provide efficient self-stabilising cellular automata with or without additional symbols that wash out finite perturbations in linear or quadratic time, but also show that there are examples of local constraints for which the self-stabilisation problem is inherently hard. We note that the optimal self-stabilisation speed is the same for all local constraints that are isomorphic to one another. We also consider probabilistic cellular automata rules and show that in some cases, the use of randomness simplifies the problem. In the deterministic case, we show that if finite perturbations are corrected in linear time, then the cellular automaton self-stabilises even starting from a random perturbation of a valid configuration, that is, when errors in the initial configuration occur independently with a sufficiently low density.
TL;DR: In this article , a coarsened version of one of the standard majority identifiers is presented. But the authors focus on the initial majority identification task and do not consider the complexity of the majority identification problem.
Abstract: The initial majority identification task is a fundamental test problem in cellular automaton research. To pass the test, a two-state automaton has to attain a uniform configuration consisting of only the state that was initially in the majority. It does so solely through its local, internal dynamics—i.e., success in the task is an example of emergent computation. Finding new, better-performing automata continues to be of interest for what additional clues they might reveal about this form of computation. Here we describe a novel, coarsened version of one of the standard majority identifiers. We show that this coarsened system outperforms its parent automaton while significantly reducing the number of computations required to accomplish the task.
27 May 2022
TL;DR: In this paper , the one-dimensional dynamics of identical discrete elements that combine the properties of newtonian mechanical particles and cellular automata are investigated, and it is shown that the motion of a cluster of combined discrete elements, which is the simplest observable object of the model, leads to the Feynman chessboard model whose continuous limit gives the Dirac equation.
Abstract: The one-dimensional dynamics of identical discrete elements that combine the properties of newtonian mechanical particles and cellular automata are investigated. It is shown that the motion of a cluster of combined discrete elements, which is the simplest observable object of the model, leads to the Feynman chessboard model whose continuous limit gives the Dirac equation.
TL;DR: In this paper , the authors study the dynamic and complexity of the generalized Q2R automaton and show the existence of non-polynomial cycles as well as its capability to simulate with synchronous update the classical version of the automaton updated under a block sequential update scheme.