1. Models of Computation for Embedded System Design Alvise Bonivento

2. Outline Goals MOCs Discrete Events Dataflow Process Networks Petri Nets Synchronous/Reactive Communicating Synchronous FSM Labeled Transition Systems SDL Process Networks Hybrid Systems CFSM Conclusions

3. Goals First step in embedded system design: specification process Formal representation helps MOCs: efficiency, formal verification, design refinement, optimization and implementation TSM: framework to compare MOCs

4. MOCs A mathematical description that has a syntax and rules for computation of the behavior described by the syntax (semantics). Used to specify the semantics of computation and concurrency. Characteristics: compact description, fidelity to design style, synthesize and optimize behavior to an implementation. Language & MOCs: MOC affects expressiveness, trade off.

5. Discrete Event (DE) Totally ordered events Digital Hardware simulators: Verilog, VHDL. Efficient for large systems, but challenged by simultaneous events ABCABC ABCABC t t t t t t+Δ VHDL: delta step solution

6. Dataflow Process Networks Directed graph: actors, streams and tokens Process sequence of firings Firings organized into a list and scheduled One cycle through the schedule back to original state DSP problems ACD B A B C D

7. Petri Nets Process control, asynchronous communication and scheduling: avoids state explosion token place transition The state of a PN is the marking Transition fire when all the predecessors are marked When firing occurs, the predecessors decrement their marking and the successors increase it. p0 p1 p2 p3p4 p5 p6 t0 t1t2 t3 t4 t5 t6

8. Petri Nets: example p0 p1 p2 p3p4 p5 p6 t0 t1t2 t3 t4 t5 t6

9. Synchronous/Reactive All signals have events with identical tags (synchronous) All signals have events at every clock tick Cycle based models (clocked-synchronous circuit) Esterel

10. Synchronous & Multirate WCDMA cell simulators User 1 User 2 User N DSP Base Station

11. Communicating Synchronous FSM FSM consists of: – Set of input symbols – Set of output symbols – Finite set of states with an initial state – Input symbols & states output symbols – Input symbols & states next states Synchronous Sequential behavior vs. state explosion – Hierarchy, concurrency, non-determinism

12. Other models Labeled Transition Systems (LTS) – CSP, CCS – Communication is based on rendevouz – Single LTS is an interleaved asynchronous model SDL Process Networks – Specification, simulation and design of TLC protocols Hybrid Systems – FA where each state is associated with a set of differential equations – When inequalities are satisfied transition may fire – Non-linear dynamic systems

13. Synchrony vs. Asynchrony Basic operation: at each clock tick, each module reads inputs, computes and produces outputs simultaneously. Triggering & Ordering: all modules are triggered to compute at every clock tick., makes verification easier System solution: unique solution at each clock tick, makes verification easier. expensive Implementation cost: may be expensive, clock rate not optimized. Basic operation: events with a non-zero amount of time between them, each process may take an arbitrary time. Triggering & Ordering: triggered to run only when inputs change. difficult to analyze System solution: difficult to analyze. cheapermore flexible Implementation cost: cheaper and more flexible.

14. CFSMCFSM Globally asynchronous, locally synchronous (GALS). POLIS. CFSM has: – A finite state machine part: inputs, outputs, states, transition and output relation. – A data computation part: reference in the transition relation to external, combinational functions. – Locally synchronous behavior: each CFSM executes a transition by producing a single output reaction in zero time. – Globally asynchronous behavior: each CFSM reads inputs, executes a transition and produces outputs in an unbounded but finite amount of time. Asynchronous interaction from a system perspective.

15. CFSM Timing behavior: – a global scheduler controls the interaction of the CFSMs. – During an execution a CFSM reads its inputs, performs a computation, possibly changes states and writes its outputs. – Each input signal is read at most once,each input event is cleared at every execution. – Input events are read atomically. Functional behavior: – Determined by the specified transition relation (TR)

16. CFSM: example A B C i o i1 i2 err Inputs arrive at a regular rate of Ni time units. Each CFSM process at a regular rate of Nr if no errors or 2Nr in case of errors. No missed event constraint.

17. Conclusions No single agreed upon standard MOC. CFSM with initially unbounded FIFO buffers: – GALS – Unbounded buffers allows static and quasi static scheduling whenever possible. – Keep buffers lossy in the formal model and give the designer tools to verify a priori if any loss occurs. – Enforce no loss for some buffers in the implementation. – Capture most of the features of the different MOCs. Multiple languages with semantics in terms of CFSMs: – Multiple scheduling, allocation, partitioning, HW & SW synthesis algorithm can be applied. Formal verification throughout the design process.