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The first-order theory of automatic sequences with addition is decidable, and this means that one can often prove combinatorial properties of these sequences "automatically", using the free software Walnut written by Hamoon Mousavi. In this talk I will explain how this is done, using as an example the measure of minimize size string attractor, introduced by Kempa and Prezza in 2018. Using the logic-based approach, we can also prove more general properties of string attractors for automatic sequences. This is joint work with Luke Schaeffer.

Spiking neural P systems (in short, SN P systems) are membrane computing models inspired by the pulse coding of information in biological neurons. SN P systems with standard rules have neurons that emit at most one spike (the pulse) each step, and have either an input or output neuron connected to the environment. A variant known as SN P modules generalize SN P systems by using extended rules (more than one spike can be emitted each step) and a set of input and output neurons. In this work we continue relating SN P modules and finite automata. In particular, we amend and improve previous constructions for the simulatons of deterministic finite automata and state transducers. Our improvements reduce the number of neurons from three down to one, so our results are optimal. We also simulate finite automata with output, and we use these simulations to generate automatic sequences.

Spiking neural P systems (in short, SN P systems) are membrane computing models inspired by the pulse coding of information in biological neurons. SN P systems with standard rules have neurons that emit at most one spike (the pulse) each step, and have either an input or output neuron connected to the environment. A variant known as SN P modules generalize SN P systems by using extended rules (more than one spike can be emitted each step) and a set of input and output neurons. In this work we continue relating SN P modules and finite automata. In particular, we amend and improve previous constructions for the simulatons of deterministic finite automata and state transducers. Our improvements reduce the number of neurons from three down to one, so our results are optimal. We also simulate finite automata with output, and we use these simulations to generate automatic sequences.

Spiking neural P systems (in short, SN P systems) are membrane computing models inspired by the pulse coding of information in biological neurons. SN P systems with standard rules have neurons that emit at most one spike (the pulse) each step, and have either an input or output neuron connected to the environment. A variant known as SN P modules generalize SN P systems by using extended rules (more than one spike can be emitted each step) and a set of input and output neurons. In this work we continue relating SN P modules and finite automata. In particular, we amend and improve previous constructions for the simulatons of deterministic finite automata and state transducers. Our improvements reduce the number of neurons from three down to one, so our results are optimal. We also simulate finite automata with output, and we use these simulations to generate automatic sequences.

Spiking neural P systems (in short, SN P systems) are membrane computing models inspired by the pulse coding of information in biological neurons. SN P systems with standard rules have neurons that emit at most one spike (the pulse) each step, and have either an input or output neuron connected to the environment. A variant known as SN P modules generalize SN P systems by using extended rules (more than one spike can be emitted each step) and a set of input and output neurons. In this work we continue relating SN P modules and finite automata. In particular, we amend and improve previous constructions for the simulatons of deterministic finite automata and state transducers. Our improvements reduce the number of neurons from three down to one, so our results are optimal. We also simulate finite automata with output, and we use these simulations to generate automatic sequences.

Spiking neural P systems (in short, SN P systems) are membrane computing models inspired by the pulse coding of information in biological neurons. SN P systems with standard rules have neurons that emit at most one spike (the pulse) each step, and have either an input or output neuron connected to the environment. A variant known as SN P modules generalize SN P systems by using extended rules (more than one spike can be emitted each step) and a set of input and output neurons. In this work we continue relating SN P modules and finite automata. In particular, we amend and improve previous constructions for the simulatons of deterministic finite automata and state transducers. Our improvements reduce the number of neurons from three down to one, so our results are optimal. We also simulate finite automata with output, and we use these simulations to generate automatic sequences.

Spiking neural P systems (in short, SN P systems) are membrane computing models inspired by the pulse coding of information in biological neurons. SN P systems with standard rules have neurons that emit at most one spike (the pulse) each step, and have either an input or output neuron connected to the environment. A variant known as SN P modules generalize SN P systems by using extended rules (more than one spike can be emitted each step) and a set of input and output neurons. In this work we continue relating SN P modules and finite automata. In particular, we amend and improve previous constructions for the simulatons of deterministic finite automata and state transducers. Our improvements reduce the number of neurons from three down to one, so our results are optimal. We also simulate finite automata with output, and we use these simulations to generate automatic sequences.

Spiking neural P systems (in short, SN P systems) are membrane computing models inspired by the pulse coding of information in biological neurons. SN P systems with standard rules have neurons that emit at most one spike (the pulse) each step, and have either an input or output neuron connected to the environment. A variant known as SN P modules generalize SN P systems by using extended rules (more than one spike can be emitted each step) and a set of input and output neurons. In this work we continue relating SN P modules and finite automata. In particular, we amend and improve previous constructions for the simulatons of deterministic finite automata and state transducers. Our improvements reduce the number of neurons from three down to one, so our results are optimal. We also simulate finite automata with output, and we use these simulations to generate automatic sequences.

Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences form a particularly interesting class of streams that live in both worlds at the same time: they are defined in terms of finite automata, which are basic computational structures in computer science; and they appear in mathematics in many different ways, for instance in number theory. Examples of automatic sequences include the celebrated Thue-Morse sequence and the Rudin-Shapiro sequence. In this paper, we apply the coalgebraic perspective on streams to automatic sequences. We shall show that the set of automatic sequences carries a final coalgebra structure, consisting of the operations of head, even, and odd. This will allow us to show that automatic sequences are to (general) streams what rational languages are to (arbitrary) languages.

Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences form a particularly interesting class of streams that live in both worlds at the same time: they are defined in terms of finite automata, which are basic computational structures in computer science; and they appear in mathematics in many different ways, for instance in number theory. Examples of automatic sequences include the celebrated Thue-Morse sequence and the Rudin-Shapiro sequence. In this paper, we apply the coalgebraic perspective on streams to automatic sequences. We shall show that the set of automatic sequences carries a final coalgebra structure, consisting of the operations of head, even, and odd. This will allow us to show that automatic sequences are to (general) streams what rational languages are to (arbitrary) languages.

In this work we show the development of Grafcet diagrams to describe the automatic sequence in a hydroelectric power plant of the national interconnected power system. The focus of this work is centered in the methodology utilized and some Grafcet diagram obtained for the sequences of shut down of the generation unity. We show than the utilization of Grafcet diagrams is possible to achieve the operation in the plant, to have a major understanding of the automatism and to facilitate the understanding of the plant for the new technical personnel., En este trabajo se muestra el desarrollo de los diagramas Grafcet (Gráfico funcional de control de etapas y transiciones) que describen el accionamiento de una unidad de generación hidroeléctrica del Sistema Interconectado Nacional. El enfoque del trabajo se centra en la metodología utilizada y en algunos diagramas Grafcet obtenidos para el caso de paro normal de la unidad de generación. Se demuestra que, con la utilización de estos diagramas, es posible mejorar la operación de la planta, lograr un mayor entendimiento del accionamiento y facilitar el entrenamiento de nuevo persona

In this work we show the development of Grafcet diagrams to describe the automatic sequence in a hydroelectric power plant of the national interconnected power system. The focus of this work is centered in the methodology utilized and some Grafcet diagram obtained for the sequences of shut down of the generation unity. We show than the utilization of Grafcet diagrams is possible to achieve the operation in the plant, to have a major understanding of the automatism and to facilitate the understanding of the plant for the new technical personnel., En este trabajo se muestra el desarrollo de los diagramas Grafcet (Gráfico funcional de control de etapas y transiciones) que describen el accionamiento de una unidad de generación hidroeléctrica del Sistema Interconectado Nacional. El enfoque del trabajo se centra en la metodología utilizada y en algunos diagramas Grafcet obtenidos para el caso de paro normal de la unidad de generación. Se demuestra que, con la utilización de estos diagramas, es posible mejorar la operación de la planta, lograr un mayor entendimiento del accionamiento y facilitar el entrenamiento de nuevo persona

In this work we show the development of Grafcet diagrams to describe the automatic sequence in a hydroelectric power plant of the national interconnected power system. The focus of this work is centered in the methodology utilized and some Grafcet diagram obtained for the sequences of shut down of the generation unity. We show than the utilization of Grafcet diagrams is possible to achieve the operation in the plant, to have a major understanding of the automatism and to facilitate the understanding of the plant for the new technical personnel., En este trabajo se muestra el desarrollo de los diagramas Grafcet (Gráfico funcional de control de etapas y transiciones) que describen el accionamiento de una unidad de generación hidroeléctrica del Sistema Interconectado Nacional. El enfoque del trabajo se centra en la metodología utilizada y en algunos diagramas Grafcet obtenidos para el caso de paro normal de la unidad de generación. Se demuestra que, con la utilización de estos diagramas, es posible mejorar la operación de la planta, lograr un mayor entendimiento del accionamiento y facilitar el entrenamiento de nuevo persona

We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are 2-regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of 2) contains an overlap.

We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are 2-regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of 2) contains an overlap.