The TASM Language Reference Manual Version 1.1 - Synrc

RC 1 ⊙ RC 2 = (rc 11 , . . . , rc 1n ) ⊙ (rc 21 , . . . , rc 2n )
= (rc 11 ⊙ rc 21 , . . . , rc 1n ⊙ rc 2n )
= ((rr 11 , rac 11 ) ⊙ (rr 21 , rac 21 ), . . . ,
(rr 1n , rac 1n ) ⊙ (rr 2n , rac 2n ))
= ((rr 11 , rac 11 ⊙ rac 21 ), ...
((rr 1n , rac 1n ⊙ rac 2n ))
The parallel composition of resources is assumed to be additive, as in the case of
hierarchical composition using the ⊗ operator:
⎧
⎪⎨ rac 1
rac 1 ⊙ rac 2 = rac 2
⎪⎩
rac 1 + rac 2
if rac 2 = ⊥
if rac 1 = ⊥
otherwise
At each global step of the simulation, a list of pending update sets are kept in an
ordered list, sorted by time of application. At each global step of the simulation, the
update set at the front of the list is composed in parallel with other update sets, using
the ⊙ operator and the resulting update set is applied to the environment. Once an
update set is applied to the environment, the step is completed and the global time of
the simulation progresses according to the duration of the applied update set.
Because each ASM step can take arbitrarily long, checking consistency of the update
sets involves a few more criteria (t ij denotes the duration of step i of machine j,
T RU ij denotes the update set for step i of machine j):
• For any pair of update sets occurring at the same global time t: ((t in , RC in , U in ), (t jm , RC jm , U jm ))
if t in < t jm then for all future update sets (t kn , RC kn , U kn ) such that ∑ p
k=i t kn ≤ t jm ,
the update sets ((t jm , RC jm , U jm ), (t kn , RC kn , U kn )) must be consistent.
What this criterion means is that consistency of updates made to global state must
be preserved through overlapping time intervals of parallel machines. For example,
if two machines write to the same environment variable, they need to do so at different
non-overlapping global times. For execution to be well-defined, there must be
no conflicting writes, meaning that overlapping update sets must be consistent. Parallel
composition, combined with time specification, enables the specification of both
synchronous and asynchronous systems.
The extreme cases of this modified formalism resolve to the base case multi-agent
ASMs. In the timed multi-agent ASM formalism, if all concurrent machines take the
same positive amount of time for each step (For all i, j, k : t ij > 0 and t kj > 0 and
t ij = t kj ) at every step, then the system is essentially a synchronous multi-agent ASM
system with linear time progression (with dt = t ij ). If all agents take a zero amount of
time at every step (For all i, j : t ij = 0), then the system is essentially an asynchronous
multi-agent ASM system with no time progression.
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