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Computing with Truly Asynchronous Threshold Logic Networks
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present simulation mechanisms by which any network of threshold logic units with either symmetric or asymmetric interunit connections (i.e., a symmetric or asymmetric "Hopfield net") can be simulated on a network of the same type, but without any a priori constraints on the order of upd ..."
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Cited by 20 (7 self)
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We present simulation mechanisms by which any network of threshold logic units with either symmetric or asymmetric interunit connections (i.e., a symmetric or asymmetric "Hopfield net") can be simulated on a network of the same type, but without any a priori constraints on the order of updates of the units. Together with earlier constructions, the results show that the truly asynchronous network model is computationally equivalent to the seemingly more powerful models with either ordered sequential or fully parallel updates.
The Computational Power of Discrete Hopfield Nets with Hidden Units
 Neural Computation
, 1996
"... We prove that polynomial size discrete Hopfield networks with hidden units compute exactly the class of Boolean functions PSPACE/poly, i.e., the same functions as are computed by polynomial spacebounded nonuniform Turing machines. As a corollary to the construction, we observe also that networks wi ..."
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Cited by 12 (6 self)
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We prove that polynomial size discrete Hopfield networks with hidden units compute exactly the class of Boolean functions PSPACE/poly, i.e., the same functions as are computed by polynomial spacebounded nonuniform Turing machines. As a corollary to the construction, we observe also that networks with polynomially bounded interconnection weights compute exactly the class of functions P/poly, i.e., the class computed by polynomial timebounded nonuniform Turing machines.
Combinatorics of Boolean automata circuits dynamics, submitted to Discrete applied mathematics
, 2010
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 9 (5 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
On the number of attractors of Boolean automata circuits
, 2009
"... In line with elds of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is Boolean automata circuits. In the cont ..."
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Cited by 3 (3 self)
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In line with elds of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on the number of attractors of Boolean automata circuits. We prove how to obtain formally the exact value of the total number of attractors of a circuit of arbitrary size n as well as, for every positive integer p, the number of its attractors of period p depending on whether the circuit has an even or an odd number of inhibitions. As a consequence, we obtain that both numbers depend only on the parity of the number of inhibitions and not on their distribution along the circuit.
On the number of attractors of positive and negative Boolean automata circuits
, 2014
"... In line with fields of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is, Boolean automata circuits. In the ..."
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Cited by 3 (2 self)
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In line with fields of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is, Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on the number of attractors of Boolean automata circuits. We prove how to obtain formally the exact value of the total number of attractors of a circuit of arbitrary size n as well as, for every positive integer p, the number of its attractors of period p depending on whether the circuit has an even or an odd number of inhibitions. As a consequence, we obtain that both numbers depend only on the parity of the number of inhibitions and not on their distribution along the circuit.
On the convergence of Boolean automata networks without negative cycles
"... Abstract. Since the 1980’s, automata networks have been at the centre of numerous studies, from both theoretical (around the computational abilities) and applied (around the modelling power of real phenomena) standpoints. In this paper, basing ourselves on the seminal works of Robert and Thomas, we ..."
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Cited by 1 (1 self)
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Abstract. Since the 1980’s, automata networks have been at the centre of numerous studies, from both theoretical (around the computational abilities) and applied (around the modelling power of real phenomena) standpoints. In this paper, basing ourselves on the seminal works of Robert and Thomas, we focus on a specific family of Boolean automata networks, those without negative cycles. For these networks, subjected to both asynchronous and elementary updating modes, we give new answers to well known problems (some of them having already been solved) about their convergence towards stable configurations. For the already solved ones, the proofs given are much simpler and neater than the existing ones. For the others, in any case, the proofs presented are constructive.