Semantics of LOTOS Answering the question: Which processes are equivalent? Basic LOTOS: ignore ! and ?...pure synchronization Dining philosophers example: –think: t –hungry: h –eat: e –give-up: g

Three versions of a Philosopher (1) PH = (t;h;g;PH) [] (t;h;e;PH) (2) PH = t; ((h;g;PH) [] (h;e;PH)) (3) PH = t;h;((g;PH) [] (e;PH)) Are these `the same’?

Trace Semantics A process defines a collection of traces YES, all three are equal (because they define the same set of traces) Insufficient when we use as building blocks and consider deadlocks with other processes

Testing/Refusal/Failure Semantics Many versions, one basic idea: a process defines `observable behaviors’, where possible failure or deadlock is observable. Is there a `test’ (a process executing in parallel) that distinguishes between 2 processes? If not, they are equivalent. (1) and (2) CAN fail in parallel with T = t;h;e;T but (3) succeeds

Bisimulation Semantics `Structural equivalence’: there is a matching from nodes of one to nodes of the other such that from any matching pair of nodes can continue with the same sequences and reach points that match. Some versions ignore internal `i’ actions (1), (2), and (3) are all different: no matching works!

Practical Implications Tools that check whether one specification is `equivalent’ to another using one of the possible semantic definitions. Various definitions are possible, for different contexts. Abstractions that build simpler versions that can be checked for temporal properties. Used for communication protocols/ mobile phones

Summary on LOTOS A Process Algebra (others: CSP and CCS) A “building block” approach, with parametric components Often uses equivalence to a simpler version as a specification for a complex system Allows considering various communication and synchronization architectures Needs to be combined with a notation for operations on data, and for fairness/liveness