The TASM Language Reference Manual Version 1.1 - Synrc

Clearly, the overlap of update sets will most likely lead to multiple consistency
violations if granularity is coarse and care is not taken into the design of the steps.
However, the consistency violations should yield insight into the parallelism and timing
characteristics of the application being studied. This insight will be preserved as
granularity is increased. The use of the next keyword in specifications changes meaning
slightly in the case of parallel machines. In the multi-agent case, the next keyword
means that a machine waits for a move by another agent, regardless of whether or not
the move affects the given machine’s execution.
Parallel composition also introduces contention between machines for resource
consumption. In the TASM language, no machine is preempted from using a resource.
However, if the resource is exhausted, an exception is thrown and results in update set
inconsistency. The shared resource model is simple and useful to model many resource
types.
Concurrent resource usage is assumed to be additive. For example, if, in a time
interval, two different machines use the same resource (in amounts r 1 and r 2 respectively),
the total amount used would be r 1 + r 2 .
Formally, we introduce the ⊙ operator to denote the parallel composition of two
update sets produced by two main machines that yield update sets with different durations:
• Update set by machine 1: T RU1 = (t1, RC1, U1)
• Update set by machine 2: T RU2 = (t2, RC2, U2)
• State when update set is produced: T RS i = (gt i , RC i , S i )
• if t1 = t2
– Combined update set: T RU = T RU1 ⊙ T RU2 = (t1, RC1 + RC2, U1 ∪
U2)
– T RS i+1 = T RS i ◦ T RU = (gt i + t1, RC i + RC1 + RC2, S i ⊙ (U1 ∪
U2)
• if t1 > t2
– Combined update set: T RU i = T RU1 ⊙ T RU2 = (t1, RC1 + RC2, U1)
– Combined update set: T RU i+1 = T RU1 ⊙ T RU2 = (t2 - t1, RC1, U2)
– T RS i+1 = T RS i ◦ T RU i = (gt i + t1, RC i + RC1 + RC2, S i ⊙ U1)
– T RS i+2 = T RS i+1 ◦ T RU i+1 = (gt i + t2, RC i + RC2, S i+1 ◦ U2)
• if t1 < t2
– Combined update set: T RU i = T RU1 ⊙ T RU2 = (t2, RC1 + RC2, U2)
– Combined update set: T RU i+1 = T RU1 ⊙ T RU2 = (t1 - t2, RC2, U1)
– S i+1 = T RS i ◦ T RU i = (gt i + t2, RC i + RC1 + RC2, S i ◦ U2)
– S i+2 = T RS i+1 ◦ T RU i+1 = (gt i + t1, RC i + RC1, S i+1 ◦ U1)
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