The TASM Language Reference Manual Version 1.1 - Synrc

of resource usage for the step. If a resource is specified as an interval, rac is a value
taken from the interval. The symbol T RU i is used to denote the timed update set, with
resource usage, of the i th step, where t i is the step duration, RC i is the set of consumed
resources, and U i is the update set:
T RU i = (t i , RC i , U i )
The execution semantics are also extended to reflect resource usage. Because resources
are limited quantities, if an executing ASM utilizes more than a resource’s
limits, execution halts. Execution is well-defined only if resource utilization falls below
the boundaries of the available resources. Resource usage is slightly different than
time in that the resource utilization for a given update set starts with the time of the previous
update set and lasts through the rule completion. The consumption of a resource
for an update set T RU i lasts during an open interval (gt i−1 , gt i ].
The state definition is also extended to reflect resource consumption:
T RS i = (gt i , SRC i , S i )
The sequence of states for a run that ends after n steps:
T RS 1 , T RS 2 , . . . , T RS n
For update sets with resources, the ◦ operator is defined as follows:
T RS i = T RS i−1 ◦T RU i = (gt i−1 , RC i−1 , S i−1 )◦(t i , RC i , U i ) = (gt i−1 +t i , RC i , S i−1 ◦U i )
For all gt in the open interval (gt i−1 , gt i ), the state T RS will be (gt, RC i , S i−1 ).
This definition reflects the behavior that resource consumption will begin with the start
of a rule execution and will last until the rule execution is finished.
The example from section 2.2 is extended to reflect the time and resource consumption
behavior. The example is listed in TASM example 2. The example uses two
resources, processor usage and memory usage.
Three sample update sets for different initial conditions of variable values are
shown below:
• Initial condition: ((light, OFF), (switch, UP))
Update set: ((5, ((memory, 200), (processor, 25)), ((light, ON))))
• Initial condition: ((light, ON), (switch, DOWN))
Update set: ((6, ((memory, 100), (processor, 15)), ((light, OFF))))
• Initial condition: ((light, OFF) (switch, DOWN))
Update set: ((0, ((memory, 0), (processor, 0)), ∅))
Formally, we can express the behavior and state progression of the first set of initial
conditions as follows:
• T RS 0 = (0, ((memory, 0), (processor, 0)), ((light, OF F ), (switch, UP )))
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