1. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 1 Lamport ’s State Machines Formal Specifications of Complex Systems CS236368 Spring 2004 Shmuel Katz The Technion titleBoth on mastertitleBoth on master

2. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 2 Specifying Concurrent Modules Classic paper by Leslie Lamport, ACM TOPLAS, vol. 5, no. 2, 1983 Texual, parametric state machine Insight on overlapping, interference For concrete program unit, like Larch interface, but reactive assumes sequential data structures

3. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 3 Open versus Closed systems A Closed system has all components inside the specification, and a simple interface to an Environment An Open system has “unknown” assignments, messages, events at any time. Much harder to specify and show correct, but sometimes necessary. When do operations take effect?

4. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 4 Overlapping Can Be Tricky Initially x = 0 Execute x := x+1 in parallel with x:= x+2. What are the possible results? The answer can depend on what is considered ‘atomic’ Many systems today have multiple processes (sometimes with time sharing)

5. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 5 Shared Memory Concurrency Multiple processes that change the same variables (operate over the same state) Have to consider what happens DURING an implementation....input/output is not enough. New issues: > waiting, > deadlock, > mutual exclusion, > starvation

6. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 6 Basic set-up Have sets of atomic actions First part--for safety properties Later--temporal logic for liveness Get values of a state from State Functions, that take the state to a value. x:S --> V and at(c) are state functions. Since the domain is always the state, just write f:R where R is the range

7. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 7 Parts of a Spec. State functions f1: R1, f2: R2,... Initial conditions I1, I2,... Properties P1, P2,.... If the initial state satisfies the initial conditions, all subsequent states satisfy the properties Pi, when examined through the state functions f j. If Pi is a regular logic predicate, asserts that it is an invariant of the system.

8. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 8 Other ways of writing Pi A leaves unchanged f when Q >A: a set of actions >f: a state function >Q: a predicate >Means: if a is in A, and Q(s), s---> s’ then f(s ’) = f(s) TOP leaves unchanged stack >TOP is a set of actions, stack is a state function INREAR leaves unchanged front when ~empty

9. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 9 Allowed Changes allowed changes to g1 when Q1 g2 when Q2 A1: R1 --> S1..... Am: Rm --> Sm >gi: state functions, Qi: predicates >Ai: set of actions, Ri: predicate >Si: binary function on s, s’ pairs for any a taking s to s’, if Qi(s) and gi(s’) =/= gi(s), then for some j, a is in Aj, Rj(s), and Sj(s, s’ )

10. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 10 Allowed Changes (cont.) “If it changes, it does so in one of these ways....” Does not force change--for safety only Assume that the condition for activating is made false by the change, so we won ’t just keep repeating the same action. Use f and f’ instead of f(s) and f(s’) Assume gj’ = gj if gj’ is not in Si allowed changes to stack POP: | stack| > 0 --> stack = out’ stack’

11. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 11 Procedures and Parameter Passing Modules with procedures Can have several procedures active at once, but only one copy of each. Parameters are passed in a global variable (on purpose to show problems) SUB is in MOD, calls are from outside MOD SUB.PAR : state function for the parameter at(SUB) = control is at beginning of SUB after(SUB) = control just after last of SUB in(SUB) = control is in SUB (including at the beginning, but NOT the exit point

12. © Katz, Spring 2004 CS236368 Formal SpecificationsLecture-- Lamport 12 module SQ with sub SQUARE All of SUB with SQUARE substituted state function val: Integer at(SQUARE) ==> val = SQUARE.PAR after(SQUARE) ==> SQUARE.PAR = val unchanged val when in(SQUARE) (Above are safety properties only-- need separate guarantee of progress/ liveness)