MTSA supports a synthesising behaviour models that control a given plant to satisfy a given property. The plant is defined using an FSP composite process. The property is defined using the controllerSpec keyword.

controller ||CONTROLLER = (PLANT)~{SPECIFICATIONS}.

The specification includes various items, some are optional:

• Safety properties. These are process names that describe bad behaviour with error states. They may have been constructed using the property or ltl_property keyword)
• Assumptions. These are names of assertions that must be boolean formulae (i.e., no temporal operators) expressed in terms of fluents. An assertion A is interpreted by the synthesis procedure as []<>A.
• Liveness. As with assumptions, they are boolean formulae and are interpreted as being g preceded by []<>.
• Controllable alphabet. This is the set of events that are controllable by the controller to be synthesised.

controllerSpec NAME = {
    safety = { COMMA SEPARATED PROCESS NAMES }
    assumption = { COMMA SEPARATED ASSERTION NAMES }
    liveness = { COMMA SEPARATED ASSERTION NAMES }
    controllable = { NAME OF SET OF LABELS }
}

A concrete example

Plant = (a -> b -> d -> Plant | c -> d -> Plant | e -> AUX), 
AUX = (f -> AUX | g -> Plant).

ltl_property NoB = []!b
fluent FE = <e, {a, b, c, d, f, g}>
fluent FD = <d, {a, b, c, e, f, g}>
fluent FG = <g, {a, b, c, d, e, f}>
assert E = FE
assert D = FD
assert G = FG

controllerSpec Spec = {
	safety = {NoB}
	assumption = {G}
	liveness = {E, D}
	controllable = {a, c, e}
}

controller ||C = (Plant)~{Spec}.

Compatibility

To check if the assumptions in a controller specification are compatible (i.e., the environment can achieve the assumptions for any controller), which is diserable (see Nicolás Roque D'Ippolito, Victor Braberman, Nir Piterman, and Sebastián Uchitel. 2010. Synthesis of live behaviour models. In Proceedings of the eighteenth ACM SIGSOFT international symposium on Foundations of software engineering (FSE '10). Association for Computing Machinery, New York, NY, USA, 77–86. pdf)

checkCompatibility ||Compatible = (Plant)~{Spec}.

• Supervisory Control
• Reactive Synthesis
• DCS