Lecture 4 Models of Computation Embedded Computing Systems

Topics n n n n n Why models of computation? Structural models. Finite-state machines. Turing machines. Petri nets. Control flow graphs. Data flow models. Task graphs. Control flow models. © 2006 Elsevier

Models of computation n Models of computation: q q n Define the basic capabilities of an abstract computer Affect programming style No one model of computation is good for all algorithms. q Systems that use multiple programming languages are called heterogeneously programmed. © 2006 Elsevier

Aspects of models of computation n Large systems may require different models of computation for different parts. q n Models of computation can be distinguished by: q q q n Models must communicate with one another Finite state vs. infinite state Control vs. data Sequential vs. parallel Introduce models now, cover in more detail later © 2006 Elsevier

Processor graph L 1 M 2 L 3 M 4 © 2006 Elsevier

Finite state machines n 1/0 State transition graph and table are equivalent: s 1

Nondeterministic FSM n Several transitions out of a state for a given input. q q n n Equivalent to executing all alternatives in parallel. Future inputs may cause some paths to be pruned Can allow e moves---goes to next state without input. Also known as nondeterministic finite automata (NFA) © 2006 Elsevier a s 1 s 2 a

Deterministic FSM from NFA a n n n Any NFA can be transformed into a deterministic FSM. Add states for the various combinations of non-determinism. So why use NFAs? a s 1 c b s 4 s 3 nondeterministic a s 1 c s 4 © 2006 Elsevier s 2 s 12 c b s 3 deterministic

Turing machine n General model of computing: tape 1 0 0 1 1 0

Turing machine step 1. 2. 3. Read current square. Erase current square. Take state-dependent

Turing machine properties n Example program: q q n If (state = 2 and cell = 0): print 0, move left, state = 4. If (state = 2 and cell = 1): print 1, move left, state = 3. n n © 2006 Elsevier Can be implemented on many physical devices. Turing machine is a general model of computability. Can be extended to probabilistic behavior.

Turing machine properties n n Infinite tape = infinite state machine. Basic model of computability. q q n Lambda calculus is alternative model. Other models of computing can be shown to be equivalent to or proper subset of Turing machine. What advantages and disadvantages do Turing machines have compared to finite state machines? © 2006 Elsevier

Control flow graph (CFG) x=a n n n Commonly used to model program structure. Nodes are unconditionally or conditionally executed. Is this a finite state or infinite state model of computation? i = 0? x=a-b y=c+d © 2006 Elsevier

Data flow graph (DFG) n Partially-ordered computations: + -, * +, -, * +

Data flow streams n n Captures sequence but not time. Totally-ordered set of values. q n New values are appended at the end as they appear. May be infinite. + -44 88 -23 88 7 -23 447944 -28 9 © 2006 Elsevier

Firing rules n n A node may have one or more firing rules. Firing rules determine when tokens are consumed and produced. q Firing consumes a set of tokens at inputs, generates token at output. © 2006 Elsevier

Example firing rules n Basic rule fires when tokens are available at all inputs:

Data flow graph properties n n n Finite state model. Basic data flow graph

Synchronous data flow (SDF) n Lee/Messerschmitt: Relate data flow graph properties to schedulability. q q Synchronous communication between data flow nodes. Nodes may communicate at multiple rates. © 2006 Elsevier

SDF notation n n Nodes may have rates at which data are produced or

SDF example n What are the input and output rates of each node? separate

Delays in SDF graphs n n Delays do not change rates, only the amount

Kahn process network n Process has unbounded FIFO at each input: channel n n process Each channel carries a possibly infinite sequence or stream. A process maps one or more input sequences to one or more output sequences. © 2006 Elsevier

Monotonicity of Khan processes n If F(X) is the output of a processor for

Networks of processes n n A network of processes relates the streams of several processes. If I = input sequences, X = internal sequences + outputs, then network behavior fixed point behavior is q n X = F(X, I) A network of monotonic processes is a monotonic process. q Even in the presence of feedback loops. © 2006 Elsevier

Task graph properties n Not a Turning machine. q q n Possible models of execution time: q q q n No branching behavior. May be extended to provide conditionals, but still FSMs Constant. Min-max bounds. Statistical. Can model late arrivals, early departures by adding dummy processes. © 2006 Elsevier

Petri net n Parallel model of computation. place token transition arc © 2006 Elsevier

Firing rule n A transition is enabled if each place at its inputs have at least one token. q n n A transition doesn’t have to fire right away. Firing a transition removes tokens from inputs and adds a token to each output place. In general, may require multiple tokens to enable firing. © 2006 Elsevier

Properties of Petri nets n n Turing complete. Arbitrary number of tokens. q q

Communication models n n Buffered communication – assumes memory is available to store a values if the receiver is not ready to receive it Unbuffered communication – assumes no memory between the sender and receiver Blocking communication – sender waits until the receiver has the data Nonblocking communication – does no require the sender to wait until the receiver has the data © 2006 Elsevier

Sources of parallelism n n Instruction-level parallelism – from executing independent instructions in parallel Data-level parallelism – from executing the same operation on multiple pieces of data in parallel Task-level parallelism – from performing multiple tasks in parallel What are mechanisms used to exploit each type of parallelism? © 2006 Elsevier