Sara Woodworth

Asynchronous spiking neural P systems

We consider here spiking neural P systems with a non-synchronized (i.e., asynchronous) use of rules: in any step, a neuron can apply or not apply its rules which are enabled by the number of spikes it contains (further spikes can come, thus changing the rules enabled in the next step). Because the time between two firings of the output neuron is now irrelevant, the result of a computation is the number of spikes sent out by the system, not the distance between certain spikes leaving the system. The additional non-determinism introduced in the functioning of the system by the non-synchronization is proved not to decrease the computing power in the case of using extended rules (several spikes can be produced by a rule). That is, we obtain again the equivalence with Turing machines (interpreted as generators of sets of (vectors of) numbers). However, this problem remains open for the case of standard spiking neural P systems, whose rules can only produce one spike. On the other hand we prove that asynchronous systems, with extended rules, and where each neuron is either bounded or unbounded, are not computationally complete. For these systems, the configuration reachability, membership (in terms of generated vectors), emptiness, infiniteness, and disjointness problems are shown to be decidable. However, containment and equivalence are undecidable.

Normal forms for spiking neural P systems

The spiking neural P systems are a class of computing devices recently introduced as a bridge between spiking neural nets and membrane computing. In this paper we prove a series of normal forms for spiking neural P systems, concerning the regular expressions used in the firing rules, the delay between firing and spiking, the forgetting rules used, and the outdegree of the graph of synapses. In all cases, surprising simplifications are found, without losing the computational completeness - sometimes at the price of (slightly) increasing other parameters which describe the complexity of these systems.

On spiking neural p systems and partially blind counter machines

A k-output spiking neural P system (SNP) with output neurons, O1, ..., Ok, generates a tuple (n1, ..., nk) of positive integers if, starting from the initial configuration, there is a sequence of steps such that during the computation, each Oi generates exactly two spikes a a (the times the pair a a are generated may be different for different output neurons) and the time interval between the first a and the second a is ni. After the output neurons generate their pairs of spikes, the system eventually halts. We give characterizations of sets definable by partially blind multicounter machines in terms of k-output SNPs operating in a sequential mode. Slight variations of the models make them universal.

Characterizations of some restricted spiking neural p systems

A k-output spiking neural P system (SNP) with output neurons, O1, ⋯, Ok, generates a tuple (n1, ⋯, nk) of positive integers if, starting from the initial configuration, there is a sequence of steps such that during the computation, each Oi generates exactly two spikes a a (the times the pair a a are generated may be different for different output neurons) and the time interval between the first a and the second a is ni. After the output neurons have generated their pairs of spikes, the system eventually halts. Another model, called k-train SNP, has only one output neuron. It generates a k-tuple (n1, ⋯, nk) if, starting from the initial configuration, the output neuron O generates the spike train aa ⋯a with exactly k+1 as such that the interval between the itha and the i+1sta is ni, and the system eventually halts. We assume, without loss of generality, that each neuron in the SNP is either bounded or unbounded. (Bounded here means that there is a fixed constant c such that at any time during the computation, the number of spikes in the neuron is at most c. Otherwise, the neuron is unbounded.) It is known that 1-output SNPs (= 1-train SNPs) are universal, i.e., they generate exactly the recursively enumerable sets over N. Here, we show the following: 1. For k ≥1, a set Q⊆Nk is semilinear if and only if it can be generated by a k-output SNP, where every unbounded neuron satisfies the property that once it starts “spiking” it will no longer receive future spikes (but can continue spiking). This result also holds for k-train SNP. 2. The set Q = {(m,2m) | m ≥1} (which is semilinear) cannot be generated by any 2-output bounded SNP (i.e., SNP all of whose neurons are bounded). Thus, for k ≥2, there are semilinear sets over Nk that cannot be generated by k-output bounded SNPs. This contrasts a known result that 1-output bounded SNPs generate all semilinear sets over N. 3. For k ≥2, k-output bounded SNPs are computationally more powerful than k-train bounded SNPs. (They are identical when k=1.) 4. For k ≥1, k-output bounded SNPs and k-train bounded SNPs can be characterized by certain classes of nondeterministic finite automata with strictly monotonic counters.

Spiking neural p systems: some characterizations

We look at the recently introduced neural-like systems, called SN P systems. These systems incorporate the ideas of spiking neurons into membrane computing. We study various classes and characterize their computing power and complexity. In particular, we analyze asynchronous and sequential SN P systems and present some conditions under which they become (non-)universal. The non-universal variants are characterized by monotonic counter machines and partially blind counter machines and, hence, have many decidable properties. We also investigate the language-generating capability of SN P systems.

On spiking neural P systems and partially blind counter machines

A k-output spiking neural P system (SNP) with output neurons,

Characterizations of some classes of spiking neural P systems

{{O_1},\ldots{,{O_k}}}

On symport/antiport P systems with a small number of objects

, generates a tuple