URP 67* WR SULPLWLYH 0HDO\)60 &RQFHSW DQG EDVLF GHILQLWLRQV On the way from the STG to an XBM solution we first derive an FSM that represents the causally specified behaviour in the EHVW SRVVLEOH VHTXHQWLDO way, i.e. completely, without additions, and such that the original causal relations can still be identified. The most general FSM of this kind is one which has what will be called the process-preserving (PP) property: It can generate -with the addition of state transitions -DOO WKRVH DQG RQO\ WKRVH level-oriented WHPSR UDO LQSXWRXWSXW VHTXHQFHV that are consistent with the causal specification, conform to fundamental-mode operation, and specify only a single suitable (quasi-)ordering for each set of concurrent output edges. -The present section will explain how to construct a SULPLWLYH 0HDO\-type FSM with the PP property from the STG.A Mealy-FSM is a sextuple M = (,,2,6,δ,λ,S 1 ), where ,, 2, and 6 are finite sets of inputs, outputs, and internal states, respectively; δ: , x 6 → 6 is the next-state function, λ: , x 6 → 2 is the output function, and S 1 ∈ 6 is the initial state. -The Mealy-FSM is primitive iff every S i ∈ 6 is stable under at most one I k ∈ , (i.e. iff there is at most one stable total state (S i , I k ) per row of the flow table). -The flow table of a primitive Mealy-FSM will be called primitive flow table (PFT) [1], and its graph a primitive state transition graph (PSTG).The Mealy type is chosen with regard for the subsequent XBM synthesis; but a Moore-type FSM with the PP property could also be constructed. Primitivity is, however, essential for capturing the PP property, regardless of the FSM type. The construction algorithm consists of four steps which are explained in subsections 2.2 to 2.5.
6WHS )URP 67* WR 6S*We assume the currently established STG model (e.g.[9]) where the underlying Petri net is n-safe (n ≥ 1) and all arcs have weight 1. This STG allows the specification of causal dependence, causal independence (concurrency) and conflict (choice, exclusion). Of course, the STG should show that rising and falling edges of every signal must always alternate (consistency). We will use Petri net notation for STGs, with full rectangles for input transitions and hollow ones for output transitions. - Fig. 2.1.a shows the STG for what originally was an extended-burst-mode example from [7], but has been modified by additional signals a and z. The circuit is to answer each φ+ edge either by x+ (if conditional input c is 0) or by y+ (if c is 1 when φ+ occurs). Besides, the output edges x-and z+ have been made concurrent. -Executing such a Petri net generates causal processes represented by SRVHWV of input and output edges.
