Antonio E. Porreca

Unconventional Computation and Natural Computation

We consider the measurement of physical quantities that are thresholds. We use hybrid computing systems modelled by Turing machines having as an oracle physical equipment that measures thresholds. The Turing machines compute with the help of qualitative information provided by the oracle. The queries are governed by timing protocols and provide the equipment with numerical data with (a) infinite precision, (b) unbounded precision, or (c) finite precision. We classify the computational power in polynomial time of a canonical example of a threshold oracle using non-uniform complexity classes.

Sublinear-Space p systems with active membranes

We introduce a weak uniformity condition for families of P systems, DLOGTIME uniformity, inspired by Boolean circuit complexity. We then prove that DLOGTIME-uniform families of P systems with active membranes working in logarithmic space (not counting their input) can simulate logarithmic-space deterministic Turing machines.

Membrane Division, Oracles, and the Counting Hierarchy

Polynomial-time P systems with active membranes characterise PSPACE by exploiting membranes nested to a polynomial depth, which may be subject to membrane division rules. When only elementary leaf membrane division rules are allowed, the computing power decreases to PPP = P#P, the class of problems solvable in polynomial time by deterministic Turing machines equipped with oracles for counting or majority problems. In this paper we investigate a variant of intermediate power, limiting membrane nesting hence membrane division to constant depth, and we prove that the resulting P systems can solve all problems in the counting hierarchy CH, which is located between PPP and PSPACE. In particular, for each integer k ≥ 0 we provide a lower bound to the computing power of P systems of depth k.

Simulating Elementary Active Membranes - with an Application to the P Conjecture.

The decision problems solved in polynomial time by P systems with elementary active membranes are known to include the class \(\mathbf{P}^{\# \mathbf{P}}\). This consists of all the problems solved by polynomial-time deterministic Turing machines with polynomial-time counting oracles. In this paper we prove the reverse inclusion by simulating P systems with this kind of machines: this proves that the two complexity classes coincide, finally solving an open problem by Păun on the power of elementary division. The equivalence holds for both uniform and semi-uniform families of P systems, with or without membrane dissolution rules. Furthermore, the inclusion in \(\mathbf{P}^{\# \mathbf{P}}\) also holds for the P systems involved in the P conjecture (with elementary division and dissolution but no charges), which improves the previously known upper bound \(\mathbf{PSPACE}\).

Fixed Points and Attractors of Reaction Systems

We investigate the computational complexity of deciding the occurrence of many different dynamical behaviours in reaction systems, with an emphasis on biologically relevant problems (i.e., existence of fixed points and fixed point attractors). We show that the decision problems of recognising these dynamical behaviours span a number of complexity classes ranging from FO-uniform AC 0 to \({\Pi_2^{\rm P}}\)-completeness with several intermediate problems being either NP or coNP-complete.

Elementary Active Membranes Have the Power of Counting

P systems with active membranes have the ability of solving computationally hard problems. In this paper, the authors prove that uniform families of P systems with active membranes operating in polynomial time can solve the whole class of PP decision problems, without using nonelementary membrane division or dissolution rules. This result also holds for families having a stricter uniformity condition than the usual one.

P SYSTEMS WITH ACTIVE MEMBRANES WORKING IN POLYNOMIAL SPACE

We prove that recognizer P systems with active membranes using polynomial space characterize the complexity class PSPACE. This result holds for both confluent and nonconfluent systems, and independently of the use of membrane division rules.

Cycles and Global Attractors of Reaction Systems

Reaction systems are a recent formal model inspired by the chemical reactions that happen inside cells and possess many different dynamical behaviours. In this work we continue a recent investigation of the complexity of detecting some interesting dynamical behaviours in reaction system. We prove that detecting global behaviours such as the presence of global attractors is PSPACE - complete. Deciding the presence of cycles in the dynamics and many other related problems are also PSPACE - complete. Deciding bijectivity is, on the other hand, a coNP - complete problem.

Flattening in (Tissue) P Systems

For many models of P systems and tissue P systems, the main behavior of a specific system can be simulated by a corresponding system with only one membrane or cell, respectively; this effective construction is called flattening. In this paper we describe the main procedure of flattening for specific variants of static (tissue) P systems as well as for classes of dynamic (tissue) P systems with a bounded number of possible membrane structures or a bounded number of cells during any computation.

P systems with elementary active membranes: beyond NP and coNP

We prove that a uniform family of P systems with active membranes, where division rules only operate on elementary membranes and dissolution rules are avoided, can be used to solve the following PP-complete decision problem in polynomial time: given a Boolean formula of m variables in 3CNF, do at least √2m among the 2m possible truth assignments satisfy it? As a consequence, the inclusion PP ⊆ PMC AM(-d,-n) holds: this provides an improved lower bound on the class of languages decidable by this kind of P systems.