Understanding StateCharts in Advanced Embedded Systems

1. Advanced Embedded Systems Lecture3 Specification Languages

2. Advanced Embedded Systems 1. StateCharts • Was introduced in 1987 by David Harel; • Is based on the shared memory concept of communication; • State diagrams are a classical method for describing the behavior of finite state machines (FSM); an ex.: • Short description: • Circles indicate states; • At any time a deterministic FSM can only be in one of its states; • Edges indicate transitions and edge labels mean events; • If an event happens, the FSM will go to the state pointed by the edge; • A FSM may also generate output;

3. Advanced Embedded Systems • StateCharts is a language for describing complex systems; for that, the hierarchy concept was introduced by means of super – states; • A super – state is a state comprising other states; states included in super – states are called sub – states; • A StateCharts example ( a hierarchical form of the precedent ex.): • Super – state S contains states A, B, C, D and E; if FSM is in state Z and receives input m, it will pass to state A; if FSM is in state S (meaning state A, B, C, D or E) and receives input k, it will pass to state Z; sub – states of S can also be super – states;

4. Advanced Embedded Systems • Each state which is not composed of other states is called basic state; for each basic state S, the super – states containing S are called ancestor states; • The FSM of figure can be in only one of the sub – states of super – state S at any time; these super – states are called OR – super – states; • The figure shows that a compact representation of exception can be obtained using the hierarchy concept; • StateCharts allows a hierarchical description of systems; • The description can be represented by a tree: • The root of the tree corresponds to the system as a whole; • All inner nodes correspond to hierarchical descriptions (super – nodes); • The leaves of the hierarchy are non hierarchical descriptions; • Until now, a transition was explicitly represented by an edge, thus showing all the internal structure; no change can be further made; • If the internal structure must be hidden more mechanisms are necessary for indicating the next state;

5. Advanced Embedded Systems • Default state mechanism: it indicates, in super – states, the particular sub – state that will be entered if the super – state is entered; • History mechanism: with it, it is possible to return to the last sub – state that was active before a super – state was left;

6. Advanced Embedded Systems • The two mechanisms can be combined, as it is shown in the precedent figure; • The behavior of the FSM is: if it is in state Z and receives input m, it will enter state A if this is the first entrance in S and the last state that it was in for any other entrance; • An application of this combined mechanism is the behavior of FSM in case of an exception; k can be an exception and input m will be used for returning to the state before the exception was generated; states A, …, E can view state Z as a procedure which can be called; after executing the procedure, the return to the calling state will be done; • Specification techniques must also be able to describe concurrency; • For that, a second class of super – states, the AND – super – states, are provided by StateCharts; • Super – states S are called AND – super – states if the system containing S will be in all of the sub – states of S whenever it is in S;

7. Advanced Embedded Systems • An example with AND – super – states is in the next figure: • An answering machine performs two tasks concurrently: it monitors the line for incoming calls and the keys for user input; • In fig. the corresponding states are Lwait and Kwait; incoming calls are processed in state Lproc and the response to pressed keys is generated in state Kproc; • It is assumed that the on/ off switch, generating events key – off and key – on, is decoded separately and pushing it does not result in entering Kproc; if this switch is pushed, both the line and the key monitoring states will be left and reentered only when the machine is switched on; default states Lwait and Kwait are entered;

8. Advanced Embedded Systems • StateCharts provide timers; they are necessary for modeling time; the symbol is shown in next figure: • After the system has been in the state containing the timer, for the specified period, a time – out will occur and the system will leave the specified state; • Timers can be used hierarchically; an ex.: to describe the behavior of state Lproc; fig. shows a possible behavior of that state: • State Lproc is terminated when the caller hangs up; but if the callee hangs up first, the phone will be dead until the caller also hangs up;

9. Advanced Embedded Systems • FSM can also generate outputs; • For that, edge labels are used; the general form is: “event [condition]/ reaction”; all three parts are optional; • The reaction part describes the reaction of the FSM to a state transition; reactions can be generation of events or assignments to variables; • The condition part means a test of the values of variables or a test of the current state of the system; • The event part refers to a test of current events; events are generated internally or externally; internal events are generated as a result of some transition and are described in reaction parts; external events are usually described in the model environment; • Examples: • off – key [not in Lproc]/ on:= 0; it shows event test, condition test for a state and variable assignment; the assignment is done if the event has occurred and the condition is true;

10. Advanced Embedded Systems • [on = 1], condition test for a variable value; • The semantics of edge labels can be explained in the context of the semantics of StateCharts; • In an implementation of StateCharts (called StateMate), a StateChart description is executed in steps; each step has 3 phases: • Phase 1: the effect of external changes on conditions and events is evaluated; it includes the evaluation of functions which depend on external events; there are no state changes in this phase; phase 1 is not needed in simple cases; • Phase 2: the set of transitions that should be made in the current step is calculated; variable assignments are evaluated but the new values are assigned only to temporary variables; • Phase 3: state transitions are executed and variables obtain new values; • The separation into phases 2 and 3 is important in order to guarantee a deterministic and reproducible behavior of StateCharts models; next figure shows an example for this behavior:

11. Advanced Embedded Systems • Due to the separation in 2 phases, temporary variables, say a’ and b’, will memorize new values for a and b; in the final phase, temporary variables are copied into the user defined variables: phase 2: a’ := b; b’ := a; phase 3: a := a’; b := b’; • The consequence is that the 2 variables will be swapped each time an event e happens; this is similar, in hardware, with two cross – connected registers:

12. Advanced Embedded Systems • Without the separation into 2 phases, the result would depend on the sequence in which the assignments are performed or, in hardware, on the delays on the 2 registers; • The separation in phases is typical for languages that reflect the operation of synchronous hardware; • The 3 phases are executed for each step; steps are executed each time events or variables have changed; • The set of all values of variables, together with the set of events generated, and the current time, is defined as the status of a StateCharts model; after executing the third phase, a new status is obtained; • The visibility of events is limited to the step following the one in which they are generated; • Thus events behave like single bit values which are stored in permanently enabled registers at one clock and have effect on the values stored at the next clock; their life is limited;

13. Advanced Embedded Systems • In contrast, variables have a value until a reassignation takes place; • New values of variables are visible to all parts of the model from the step following the step in which the assignment was made; it means StateCharts semantics implies that new values of variables are propagated to all parts of the model between 2 steps; this is a broadcast mechanism for updates on variables; • In case of distributed systems it will be very difficult to update all variables between two steps and that is why StateCharts is not appropriate for modeling distributed systems; • Advantages and disadvantages of StateCharts: • It is appropriate to modeling local systems; • Capability of nesting hierarchies at different levels combined with the existence of AND and OR – states; • There are commercial tools based on StateCharts: StateMate, BetterState; they provide a complete path from StateCharts specifications to hardware; some of the tools can translate StateCharts descriptions in equivalent C or VHDL programs;

14. Advanced Embedded Systems • Frequently low efficiency for the automatic translation; • Does not include descriptions of non – functional behavior; • It is not object oriented; • Cannot describe hardware structures. 2. General language characteristics • The languages can be compared through some characteristics: • The use of non – standard I/ O devices; • Synchronism or asynchronism; • Process concepts; • Synchronization and communication; • Timing specification; • The use of non – standard I/ O devices • Some languages can directly control the I/ O devices, e.g. ADA, assembler; all I/ O operations can be programmed and also memories can be directly accessed, through the addresses; • StateCharts do not support direct access to I/ O devices but commercial implementations have this feature.

15. Advanced Embedded Systems • Synchronims and asynchronism • In some languages based on FSMs (ADA, Java) the order in which executable processes are executed is not specified (they are non – deterministic); this can affect the result and negative consequences can arise; • The non – determinism is avoided with synchronous languages; • They describe concurrently operating automata showing that if automata are in parallel, the transition of the product means the simultaneous transitions of all the parts in parallel; • It is similar with considering a single global clock for all the parts and at each pulse, all inputs are considered and transitions are made to the new states; a fast broadcast mechanism is necessary for all parts; • This is an idealistic view of concurrency but has the advantage of guaranteeing a deterministic behavior; • In the general model of FSMs, each FSM has its own clock; restriction; • Because of the single clock model, synchronous languages are difficult to use in distributed systems; • Examples of synchronous languages: Esterel, StateCharts

16. Advanced Embedded Systems • Process concepts • The process concepts in programming languages can be compared according to: • Static or dynamic number of processes: a static number of processes simplifies the implementation and is enough if each process models a hardware block and there is no dynamically change of the hardware; • Nested or at the same level processes: • Nested: process { process { process { }}} • Same level: process { process { process { • Process creation: there are different techniques: process declaration in the source code, through the fork and join mechanism and also through explicit process creation calls; • The StateCharts has static processes, nested and process creation results from an elaboration of the source code;

17. Advanced Embedded Systems • Synchronization and communication: • 2 communication paradigms: shared memory and message passing; • Shared memory: • All variables can be accessed from all processes; requires physically common memory; can be fast; • Reads to the shared memory can be free but for writing exclusive access to the memory must be guaranteed; segments of code for which exclusive access must be guaranteed are called critical sections; • There are several mechanisms for guaranteeing exclusive access to resources: semaphores, monitors, conditional critical regions etc. • Message passing: • Is slower than shared memory; does not requires physically common memory • There are 3 techniques for implementation: • Asynchronous message passing, also called non – blocking communication; • Synchronous message passing, also called blocking communication or rendez – vous communication; • Extended rendez – vous or remote invocation: the transmitter is allowed to send the message only after an acknowledgement from the receiver;

18. Advanced Embedded Systems • Timing specification: 4 types of specifications concerning the time: • Measurement of elapsed time: shows how much time has elapsed from the last call; timers are needed; • Delay of processes: for a specified time; • Timeouts specification: limit the time a process can stay in a certain state; • Deadlines and schedules: methods must exist for specifying them; • StateCharts includes only timeouts specification. 3. SDL • As opposite to StateCharts, SDL was designed for distributed applications and is based on asynchronous message passing; it models distributed systems; • It is a graphical and textual specification language; • It was standardized by ITU in 1980 and updated several times;

19. Advanced Embedded Systems • Processes are the basic elements of SDL; processes represent extended finite state machines; extensions include operations on data; next fig. shows the symbols used in the graphical form of SDL: • Next fig. shows a state diagram and its representation in SDL:

20. Advanced Embedded Systems • Variables can be declared locally for processes; • SDL contains programming language elements such as procedures; procedure calls; can also be represented graphically; • In general, SDL descriptions will consist of a set of interacting processes or FSMs; processes can send signals to other processes; • Interprocess communication is described based on FIFO queues associated with each process; signals sent to a particular process will be placed in its corresponding FIFO queue; this is the implementation of the asynchronous message passing concept;

21. Advanced Embedded Systems • A process fetch the next available entry from the FIFO queue and compares it with its inputs described for the current state; if it matches, the corresponding state transition takes place and an output is generated; if not, it is ignored; • FIFO queues are conceptually thought as being infinite, meaning the overflow is not considered; in reality, however, their length can be only finite so when implementing the specifications safe upper bounds of the FIFO queues must be provided; • Process interaction diagrams are used for visualizing the processes which are communicating; signals are sent and received on channels; in SDL, “signal” means an input or output of an automata;

22. Advanced Embedded Systems • The destination of a signal can be indicated in 3 ways: • Through process identifiers: by using identifiers of recipient processes in the graphical output symbol (fig., left); OFFSPRING identifies a child process generated dynamically by a process; • Explicitly: by indicating the channel name (fig., right); Sw1 is the name of a channel; • Implicitly: by signal names; in the fig., signal B will implicitly always communicate via channel Sw1; • Processes cannot be nested but can be grouped hierarchically into blocks; blocks at the higher level are called systems, blocks at the lowest level are called process interaction diagrams; • Next fig. shows the hierarchy modeled by the following block diagrams; the system is the root and the process interaction diagrams are the leaves;

23. Advanced Embedded Systems • The highest level in the hierarchy: • The hierarchy model:

24. Advanced Embedded Systems • In order to model time, SDL contain timers; a timer can be declared locally for processes; SET and RESET primitives set, respectively, reset a timer; • Fig. shows the use of a timer T; timer T is set to the current time plus p, during the transition from state D to state E; when transition from E to A takes place, a timer of p time units is active; if signal f arrived after the p time units have elapsed, a transition to state A is executed without generating output signal v;

25. Advanced Embedded Systems • Application: description of protocol stacks in a computer network; • The network: • The description of the protocols: • Each layer describes communication at a more abstract level; • The behavior of each layer is typically modeled as a finite state machine; the detailed description of a FSM depends on the network protocol; usually it comprises checking and handling errors and transfers of information blocks;

26. Advanced Embedded Systems • Advantages and disadvantages: • Appropriate for distributed applications; • Because the order in which FSMs are reading inputs is unknown, SDL is not deterministic; • Commercial tools, also for connecting to MSCs and UML; • Implementation requires bound for the maximum length of the FIFO queues; it may be difficult to compute; • Timer approach is adequate only for soft deadlines; • Limited way of using hierarchies; • Limited programming language support; • No description for non – functional properties. 4. Message Sequence Charts • Provide a graphical way for describing schedules; • Uses one dimension for time (usual the vertical dimension) and the other for geographical distribution;

27. Advanced Embedded Systems • MSCs is just adequate for visualizing schedules of trains and busses; the example refers to trains between Amsterdam, Cologne, Brussels and Paris; Aachen is an intermediate stop between Cologne and Brussels; • Vertical segments mean times spent at stations; for one of the trains there is a timing overlap; • Advantages and disadvantages: • Appropriate for representing schedules; • Few information about synchronization (overlap in Brussels happens coincidentally or a synchronization is desired for connecting trains ?) • Deviations from the presented schedules can hardly be included.

28. Advanced Embedded Systems 5. Petri nets • A method for modeling causal dependencies; introduced in 1962; • Do not assume global synchronization and therefore suited for modeling distributed systems; • Key elements: • Conditions: are either satisfied or not satisfied; • Events: can happen or not; • Flow relation: describes the conditions that must be met before events can happen and it also describes the conditions that become true if events happen; • Graphical notations for Petri nets use circles for conditions, boxes for events and arrows for flow relations; • The example describes mutual exclusion for trains at a railroad track that must be used in both directions: • A token is used to prevent collisions; the token is symbolized by a condition in the center of the model;

29. Advanced Embedded Systems • A filled circle indicate the condition is met, that is the track is available; • A filled circle shows, in this example, that a train wants to go to the right; • The two conditions necessary for event “train entering track from the left” are satisfied; there two conditions are called preconditions; • If the preconditions of an event are met, it can happen; as a result the token is no longer available and no train wants to enter the track; • The preconditions are no longer met and the filled circles disappear;

30. Advanced Embedded Systems • Now, there is a train going on that track from the left to the right and thus, the corresponding condition is met; • A condition which is met after an event happened is a postcondition; • An event can happen only if all its preconditions are satisfied; after the event happened the preconditions are not longer true and the postconditions become valid; arrows show which of the conditions are preconditions and postconditions; • Continuing the example, a train leaving the track will return the token to the condition at the center of the model: • Important advantages of Petri nets: • They can be the basis for formal proofs about system properties; • There are standardized ways of generating such proofs; • For that, formal definitions for Petri nets must be developed;

31. Advanced Embedded Systems • Condition/ event nets: a class of Petri nets • N = (C, E, F) is called a net, iff the following holds: C (conditions) and E (events) are disjoint sets; F  (C  E)  (E  C) is a binary relation called flow relation. • Let N be a net and let x  (CE): x := {y | y F x} is called the set of preconditions; x := {y | x F y} is called the set of postconditions; • Let (c,e)  C  E. (c,e) is called a loop iff cFe  eFc. N is called pure, if F does not contain any loops; • A net is simple if no two transitions, t1 and t2 have the same set of pre and postconditions; • Simple nets without isolated elements with some additional restrictions are called condition/ event nets; • They are a special case of bipartite graphs;

32. Advanced Embedded Systems • Place/ transition nets • For condition/ event nets, there is at most one token/ condition; • In many applications, more tokens/ condition are needed; • Nets with more tokens/ condition are called place/ transition nets; places correspond to conditions and transitions correspond to events; • The number of tokens/ place is called a marking; mathematically, a marking is a mapping of the set of places to the set of natural numbers extended by a special symbol, ω, meaning infinity; • (P, T, F, K, W, M0) is called a place/ transition net iff: N = (P, T, F) is a net with places p  P and t T; Mapping K : P → (ℕ0 {}) \{0} indicates the capacity of places; Mapping W : F → (ℕ0\{0}) indicates the weight of graph edges; Mapping M0 : P → ℕ0 {} represents the initial marking of the places; ℕ0 is the set of natural numbers plus 0; • Edge weight determines the number of tokens that are required before transitions can happen and the number of tokens that are generated if a certain transition takes place;

33. Advanced Embedded Systems • Let M(p) a current marking of p  P and M’(p) a marking after a transition t T took place; • The weight of edges belonging to preconditions: the number of tokens that are removed from places in the precondition set; the weight of edges belonging to the postcondition: the number of tokens that are added to the places in the postcondition set; • Formally, marking M’ is obtained according to the relations: • Transition tj affects the current marking:

34. Advanced Embedded Systems • Predicate/ transition nets • Condition/ event nets and place/ transition nets become very large for large examples; predicate/ transition nets allow a reduction of the size; • Example: the dining philosophers problem: • The model given by the condition/ event net: • Conditions tj = thinking states, ej = eating states, fj = available forks;

35. Advanced Embedded Systems • The model with the predicate/ transition nets: • Tokens have an identity and can be distinguished; • In fig. 3 philosophers, p1, p2 and p3, are distinguished and fork f3 is identified; • Edges can be labeled with variables and functions; in the ex. variables are used for the distinguish the philosophers and functions l(x) and r(x) are used for identifying the left and right forks of philosopher x, respectively; the 2 forks form a precondition for transition u and are returned as a postcondition for transition v; • The model can be easily extended for more than 3 philosophers simply by adding tokens; the structure of the net must not be changed;

36. Advanced Embedded Systems • Advantages and disadvantages: • Powerful for modeling causal dependencies; • All decisions can be taken locally, by analyzing transitions and their pre and postconditions; • Appropriate for modeling geographically distributed systems; • There is a strong formalism allowing proofs of system properties; • Time is not modeled; • Standard Petri nets don’t include hierarchy and programming language elements; • It is difficult to represent data; • There are extended versions of Petri nets limiting the disadvantages; • Very popular due to the spread of distributed applications.