By Zhiming Liu, Jim Woodcock, Huibiao Zhu

This Festschrift quantity, devoted to He Jifeng at the celebration of his seventieth birthday in September 2013, comprises 24 refereed papers by way of best researchers, present and previous colleagues, who congratulated at a celebratory symposium held in Shanghai, China, during the tenth overseas Colloquium on Theoretical elements of Computing, ICTAC 2013. The papers conceal a huge spectrum of topics, from foundational and theoretical issues to courses and platforms concerns and to purposes, comprising formal equipment, software program and platforms modeling, semantics, legislation of programming, specification and verification, in addition to logics.

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The SOLVE clause specifies behaviour fairly directly. For example the behaviour of pliant variable y and output o! is given by a direct assignment to the (time dependent) value of the expression E(. ). Alternatively, the behaviour of pliant variable x is given by the solution of the first order ordinary differential equation (ODE) D x = φ(. ), where D indicates differentiation with respect to time. (In fact the sematics of the y, o! = E case is given in terms of the ODE D y, D o! = D E, so that x, y and o!

He’s group at ECNU. These new kinds of system throw up novel challenges in terms of design technique, as it is proving more and more difficult to ignore the continuous characteristics in their behaviours. Specifically, such technical challenges are being increasingly felt in the context of the B-Method [2, 3], where an increasing number of applications involve continuous behaviour of some sort in an essential way. Hybrid Event-B [10] has been introduced to bring new capabilities to traditional discrete Event-B [3], in order to address the challenges referred to.

Time is modelled as an interval T of the reals. A run starts at some initial moment of time, t0 say, and lasts either for a finite time, or indefinitely. The duration of the run T , breaks up into a succession of left-closed right-open subintervals: T = [t0 . . t1 ), [t1 . . t2 ), [t2 . . t3 ), . .. The idea is that mode events (with their discontinuous updates) take place at the isolated times corresponding to the common endpoints of these subintervals ti , and in between, the mode variables are constant and the pliant events stipulate continuous change in the pliant variables.

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