Time-Free Tissue P Systems for Solving the Hamilton Path Problem

Tissue P systems are distributed and parallel computing models inspired by the communication behavior of living cells in tissues. Theoretically, tissue P systems can generate exponential working space in linear time, which makes it feasible to solve computational hard problems in polynomial time. In traditional tissue P systems, the execution of each rule takes exactly one time unit, thus making the system work synchronously. However, the restriction does not correspond with the biological fact, since biochemical reactions may vary in unpredicted conditions. In this work, we define the timed tissue P systems by adding a time mapping to each rules to specify the execution time for them. Furthermore, a uniform and time-free solution to Hamilton Path Problems is obtained by a family of such systems, where the execution time of rules can change and the output produced is always correct. abstract environment.