A processing architecture supports executing instructions in parallel after identifying at least one level of dependency associated with a set of traces within a segment of code. Each trace represents a sequence of logical instructions within the segment of code that can be executed in a corresponding operand stack. Scheduling information is generated based on a dependency order identified among the set of traces. Thus, multiple traces may be scheduled for parallel execution unless a dependency order indicates that a second trace is dependent upon a first trace. In this instance, the first trace is executed prior to the second trace. Trace dependencies may be identified at run-time as well as prior to execution of traces in parallel. Results associated with execution of a trace are stored in a temporary buffer (instead of memory) until after it is known that a data dependency was not detected at run-time.