Yun-Bum Kim

P Systems and the Byzantine Agreement

Abstract We first propose a modular framework for recursive composition of P systems. This modular approach provides encapsulation and information hiding, facilitating the design of P programs for complex algorithms. Using this framework, we developed a P program that solves the classical version of the Byzantine agreement problem, for N participants connected in a complete graph, according to the well known Byzantine agreement algorithm based on EIG trees. We prove the correctness of this modular composition and conclude with a list of open problems.

Edge- and Node-Disjoint Paths in P Systems

In this paper, we continue our development of algorithms used for topological network discovery. We present native P system versions of two fundamental problems in graph theory: finding the maximum number of edge- and node-disjoint paths between a source node and target node. We start from the standard depth-first-search maximum flow algorithms, but our approach is totally distributed, when initially no structural information is available and each P system cell has to even learn its immediate neighbors. For the node-disjoint version, our P system rules are designed to enforce node weight capacities (of one), in addition to edge capacities (of one), which are not readily available in the standard network flow algorithms.

Discovering the membrane topology of hyperdag p systems

In an earlier paper, we presented an extension to the families of P systems, called hyperdag P systems (hP systems), by proposing a new underlying topological structure based on the hierarchical dag structure (instead of trees or digraphs). In this paper, we develop building-block membrane algorithms for discovery of the global topological structure from the local cell point of view. In doing so, we propose more convenient operational modes and transfer modes, that depend only on each of the individual cell rules. Finally, by extending our initial work on the visualization of hP system membranes with interconnections based on dag structures without transitive arcs, we propose several ways to represent structural relationships, that may include transitive arcs, by simple-closed planar regions, which are folded (and possibly twisted) in three dimensional space.

New Solutions to the Firing Squad Synchronization Problems for Neural and Hyperdag P Systems

We propose two uniform solutions to an open question: the Firing Squad Synchronization Problem (FSSP), for hyperdag and symmetric neural P systems, with anonymous cells. Our solutions take e_c+5 and 6e_c+7 steps, respectively, where e_c is the eccentricity of the commander cell of the dag or digraph underlying these P systems. The first and fast solution is based on a novel proposal, which dynamically extends P systems with mobile channels. The second solution is substantially longer, but is solely based on classical rules and static channels. In contrast to the previous solutions, which work for tree-based P systems, our solutions synchronize to any subset of the underlying digraph; and do not require membrane polarizations or conditional rules, but require states, as typically used in hyperdag and neural P systems.

Synchronization in P modules

In the field of molecular computing, in particular P systems, synchronization is an essential requirement for composing or sequentially linking together congenial P system activities. We provide an improved deterministic algorithm based on static structures and traditional rules, which runs in 4e + 13 steps, where e is the eccentricity of the initiating cell. Using the same model, extended with the support of cell IDs, we provide another deterministic algorithm, which runs in 3e + 13 steps. Our algorithms use a convenient framework, called P modules, which embraces the essential features of many popular types of P systems.

An adaptive algorithm for p system synchronization

We present an improved solution for the Firing Squad Synchronization Problem (FSSP) for digraph-structured P systems. We improve our previous FSSP algorithm by allowing the general to delegate a more central cell in the P system to send the final command to synchronize. With e being the eccentricity of the general and r denoting the radius of the underlying digraph, our new algorithm guarantees to synchronize all cells of the system, between e +2r +3 steps (for all trees structures and many digraphs) and up to 3e +7 steps, in the worst case for any digraph. Empirical results show our new algorithm for tree-structured P systems yields at least 20% reduction in the number of steps needed to synchronize over the previous best-known algorithm.