Kernel P systems: From modelling to verification and testing

Abstract

A kernel P system integrates in a coherent and elegant manner some of the most successfully used features of the P systems employed in modelling various applications. It also provides a theoretical framework for analysing these applications and a software environment for simulating and verifying them. In this paper, we illustrate the modelling capabilities of kernel P systems by showing how other classes of P systems can be represented with this formalism and providing a number of kernel P system models for a sorting algorithm and a broadcasting problem. We also show how formal verification can be used to validate that the given models work as desired. Finally, a test generation method based on automata is extended to non-deterministic kernel P systems.

Translating Xd-C programs to MSVL programs

“…TER, (4) In a similar way, it can be proved that TER, (7,8) In a similar way, it can be proved that (1) α e ∼e b Theorem 1 (2) α M ∼ si given condition In a similar way, it can be proved that In the Xd-C program, the memory state transfers from M to M 2 . Compared to M , M 2 allocates memory blocks to variables y 1 , ..., y m and variables in dcl, and assigns v k to y k for 1 ≤ k ≤ m. Whereas in the MSVL program, the state transfers from s i to s t .…”

“…(ra1 aop ra2, σ, s, |σ| + 1)⇓ptr(b , j ) assumption (6) =⇒ (ra1, σ, s, |σ| + 1)⇓ptr(b , j 1 ) ∧ (ra2, σ, s, |σ| + 1)⇓n2∧ j = j 1 + n2 * sizeof (τ ) R6, (5) (7) (G, E e1, M ⇒ptr(b, j1)) ∧ (G, E e2, M ⇒v2)∧ (ra1, σ, s, |σ| + 1)⇓ptr(b , j 1 ) ∧ (ra2, σ, s, |σ| + 1)⇓n2 (4, 6) (8)…”

“…Definition 4, (7) 10. For a function call x(e 1 , ..., e k ), if x points to a user-defined function, ExT r(x(e 1 , ..., e k )) = ext f (ra 1 , ..., ra k , RV al) otherwise ExT r(x(e 1 , ..., e k )) = ext f (ra 1 , ..., ra k ), where ra i = ExT r(e i ) for 1 ≤ i ≤ k, f = ExT r(x) and all expressions are right-value expressions.…”

“…=⇒ α ptr(b, j) ∼ ptr(b , j ) Definition 2, 4, (1, 3, 4) (6) (G, E e, M ⇒v) ∧ (ra, σi−1, si, i)⇓n assumption (7) =⇒ α v ∼ n Definition 3, 4, (2, 3, 6) In the MSVL program, we have (8) s l i (xm) = (b , j ) assumption (9) (la := ra, σi−1, si, i) (12,13) {here storeval and loadval are borrowed from [26], see Appendix A.} TER, (16,17) Note that, (16) tells us the MSVL program eventually terminates and (17) indicates that final states M and s i+1 are equivalent.…”

Modelling and Validating an Engineering Application in Kernel P Systems

“…This approximation is obtained by limiting the length of any computation to an upper bound k and considering only computations up to k transitions in length. This approximation is then used to construct a deterministic finite cover automaton (DFCA) of the model [6][7][8].…”