Concurrent Execution

Transcription

1 Concurrent Execution Overview: concepts and definitions modelling: parallel composition action interleaving algebraic laws shared actions composite processes process labelling, action relabeling and hiding (these slides including graphics are a modified version of the slides from Ch3 of Magee & Kramer: Concurrency) COMP2310 Lecture 4: Concurrent Execution (I)

2 Concepts and Definitions concepts: processes - concurrent execution interleaving of actions from component processes interaction / synchronization via shared actions: both components must participate concurrency: logically simultaneous processing Does not imply multiple processing elements (cores, PE). Requires interleaved execution on a single PE parallelism: physically simultaneous processing Involves multiple PEs and/or independent device operations. both concurrency and parallelism require controlled access to shared resources we use these terms interchangeably and generally do not distinguish between real and pseudo-concurrent execution COMP2310 Lecture 4: Concurrent Execution (I)

3 Modeling Concurrency how should we model process execution speed? Arbitrary speed (we abstract away time) how do we model concurrency? Arbitrary relative order of actions from different processes (interleaving but preservation of order wrt. each process) what is the result? Provides a general model independent of scheduling (asynchronous model of execution) notation: If P and Q are processes then (P Q) represents the concurrent execution of P and Q The operator is the parallel composition operator COMP2310 Lecture 4: Concurrent Execution (I)

4 ÁÌ À Ö Ø ËÌÇÈ µº > Ø Ò > Ø Ð > ËÌÇÈ µº ÇÆÎ ÊË Concurrent Process Example: Disjoint Alphabets ÇÆÎ ÊË ÁÌ À ÁÌ À ÇÆÎ ÊË µº possible traces as a result of action interleaving: Ø Ò Ø Ð Ö Ø Ø Ò Ö Ø Ø Ð Ö Ø Ø Ò Ø Ð (2 states) (3 states) (0,0) (0,1) (0,2) (1,2) (1,1) (1,0) (2 3 states) COMP2310 Lecture 4: Concurrent Execution (I)

5 Parallel Composition Algebraic Laws commutative: (P Q) = (Q P) associative: (P (Q R)) = ((P Q) R) = (P Q R) it does not matter which order you compose processes we can drop the inner parentheses clock radio example: Ø > ÄÇ Ã µº ÄÇ Ã ÓÒ > Ó > Ê ÁÇ µº Ê ÁÇ ÄÇ Ã Ê ÁÇ ÄÇ Ã Ê ÁÇ µº LTS? Traces? Number of states? (hint: is this structurally similar to another example?) principle: in a parallel composition, each component process must undergo its own state transitions they do so independently if their alphabets are disjoint corollary: any sub-trace of (P Q) wrt. P s alphabet must also be a trace of P COMP2310 Lecture 4: Concurrent Execution (I)

6 Modeling Process Interaction: Shared Actions if the processes in a composition have actions in common, these actions are said to be shared i.e. they have non-disjoint alphabets shared actions are the way that process interaction is modeled. while unshared actions may be arbitrarily interleaved, a shared action must be executed at the same time by all processes that participate in the shared action example: Å Ã Ê synchronizes with ÍË Ê on the Ö Ý action: Ñ > Ö Ý > Å Ã Ê µº Å Ã Ê Ö Ý > Ù > ÍË Ê µº ÍË Ê Å Ã Ê ÍË Ê Å Ã Ê ÍË Ê µº LTS? Traces? Number of states? COMP2310 Lecture 4: Concurrent Execution (I)

7 Modeling Interaction - Handshake a handshake is an action acknowledging another action e.g. Ù acknowledges completion of Ù Ñ > Ö Ý > Ù > Å Ã ÊÚ¾ µº Å Ã ÊÚ¾ Ö Ý > Ù > Ù > ÍË ÊÚ¾ µº ÍË ÊÚ¾ Å Ã Ê ÍË ÊÚ¾ Å Ã ÊÚ¾ ÍË ÊÚ¾ µº 3 states 3 states 3 3 states? equivalent to ÍË ÊÚ¾ Ñ > Ö Ý > Ù > Ù > Å Ã Ê ÍË ÊÚ¾µº Å Ã Ê interaction constrains the overall behavior COMP2310 Lecture 4: Concurrent Execution (I)

8 Ã Ñ > Ö Ý > Ù > Å Ã µº Å Ã Ñ > Ö Ý > Ù > Å Ã µº Å multi-party synchronization: Modeling Interaction: Multiple Processes > > > equivalent to Ñ > Ñ > Ê ÌÇÊ Ñ Ñ > Ê µ > Ê Ö Ý > Ñ Ð > Ù > ÌÇÊ µº COMP2310 Lecture 4: Concurrent Execution (I)

9 Composite Processes a composite process is a parallel composition of primitive processes These composite processes can be used in the definition of further compositions e.g. Å Ã ÊË Å Ã Å Ã µº ÌÇÊ Å Ã ÊË ËË Å Ä µº substituting the definition for Å Ã ÊË in ÌÇÊ and applying the associative law for parallel composition results in the original definition for ÌÇÊ in terms of primitive processes COMP2310 Lecture 4: Concurrent Execution (I)

10 Process Instances and Labeling È prefixes each action label in the alphabet È of with e.g. two instances of a switch process: ÓÒ > Ó > ËÏÁÌ À µº ËÏÁÌ À ÌÏÇ ËÏÁÌ À ËÏÁÌ À ËÏÁÌ À µº an array of instances of the switch process: ËÏÁÌ À Ë Æ µ ÓÖ ÐÐ ½ºº Æ ËÏÁÌ À µº (the text and LTSAtool use the abbreviation ½ººÆ ËÏÁÌ Àµ for the RHS) this is useful to create multiple instances of primitive processes Q: can they interact with each other? Is this a problem? COMP2310 Lecture 4: Concurrent Execution (I)

11 Review Exersize: Indexed Actions and Parallel Composition A die (singular of dice) may repeatedly engage in a throw action followed by a show action, which has an integer value from 1 to 6 associated with it. Q1: what is a correct FSP model for the die? (a) Á Ø ÖÓÛ > ÓÛ > Á µº (b) Á Ø ÖÓÛ > ÓÛ ½ºº > Á µº (c) Á Ø ÖÓÛ ½ºº > ÓÛ > Á µº (d) Á Ø ÖÓÛ > ËÀÇÏ ½ºº µ ËÀÇÏ Ú ½ºº Á º Q2: how many states does it have? (a) 2 (b) 3 (c) 6 (d) 7 (e) 12 Q3: What is an FSP composition of two independent die processes? (a) Á Á Á µº (b) Á Á Á µº Q4: how many states does this have? COMP2310 Lecture 4: Concurrent Execution (I)

12 Process Labeling by a Set of Prefix Labels { ½ ºº Ü} È replaces every action label Ò in the alphabet of È with the labels ½ºÒ ººº ÜºÒ Further, every transition Ò > µ in the definition of È is replaced with the transitions { ½ºÒ ºº ܺÒ} > µ process prefixing is useful for modeling shared resources: ÕÙ Ö > Ù > Ö Ð > ÍË Ê µº ÍË Ê ÕÙ Ö > Ö Ð > Ê ËÇÍÊ µº Ê ËÇÍÊ Ê ËÇÍÊ ËÀ Ê ÍË Ê ÍË Ê { } Ê ËÇÍÊ µº { } Ê ËÇÍÊ now can interact with the two ÍË Ê processes COMP2310 Lecture 4: Concurrent Execution (I)

13 Process Prefix Labels for Shared Resources How does the model ensure that the user that acquires the resource is the one to release it? COMP2310 Lecture 4: Concurrent Execution (I)

14 Action Relabeling relabeling functions are applied to processes to change the names of action labels their general form is { Ò ÛÐ Ð 1»ÓÐ Ð Ð 1... Ò ÛÐ Ðn»ÓÐ Ð Ðn } Note that both Ò ÛÐ Ð and ÓÐ Ð Ð can be sets of labels. relabeling ensures that composed processes synchronize on particular actions ÐÐ >Û Ø >ÓÒØ ÒÙ > ÄÁ ÆÌ µº ÄÁ ÆÌ Ö ÕÙ Ø > ÖÚ >Ö ÔÐÝ >Ë ÊÎ Ê µº Ë ÊÎ Ê ÄÁ ÆÌ Ë ÊÎ Ê ÄÁ ÆÌ Ë ÊÎ Ê µ» { Ðл Ö ÕÙ Ø Ö ÔÐÝ» Û Ø}º the relabeling applies to all primitive processes in the composition (it gets applied before the ÁÁ); it is mainly used to make the primitive processes interact enables us to specify component processes in a modular way upon composition, can be used to connect processes COMP2310 Lecture 4: Concurrent Execution (I)

15 ÄÁ ÆÌ ÐÐ >Û Ø >ÓÒØ ÒÙ > ÄÁ ÆÌ µº Ö ÕÙ Ø > ÖÚ >Ö ÔÐÝ >Ë ÊÎ Ê µº Ë ÊÎ Ê Action Relabeling: Client-Server ÄÁ ÆÌ Ë ÊÎ Ê ÄÁ ÆÌ Ë ÊÎ Ê µ» { Ðл Ö ÕÙ Ø Ö ÔÐÝ» Û Ø}º alternative formulation using qualified or prefixed labels: ÔØ º Ö ÕÙ Ø > ÖÚ > ÔØ º Ö ÔÐÝ > Ë ÊÎ ÊÚ¾ Ë ÊÎ ÊÚ¾ ÐÐ º Ö ÕÙ Ø > ÐÐ º Ö ÔÐÝ > ÓÒØ ÒÙ > ÄÁ ÆÌÚ¾ µº ÄÁ ÆÌÚ¾ ÄÁ ÆÌ Ë ÊÎ ÊÚ¾ ÄÁ ÆÌÚ¾ Ë ÊÎ ÊÚ¾ µ» { Ðл ÔØ}º (the renaming is applied to the prefix) COMP2310 Lecture 4: Concurrent Execution (I)

16 Action Hiding: an Abstraction to Reduce Complexity when applied to a process È, the hiding operator \{ ½ ººº Ü} removes the action names ½,..., Ü from the alphabet of È and makes these concealed actions silent these silent actions are labeled Ø Ù silent actions in different processes are not shared when applied to a process È, the interface operator { ½ ººº Ü} hides all actions in the alphabet of È not labeled in the set ½,..., Ü (sometimes it is more convenient to specify the set of labels to be exposed) the following definitions are equivalent: ÕÙ Ö > Ù > Ö Ð > ÍË Ê µ \ { Ù }º ÍË Ê ÕÙ Ö > Ù > Ö Ð > ÍË Ê µ { ÕÙ Ö Ö Ð }º ÍË Ê The LTSAtool s minimization function removes hidden Ø Ù actions to produce an LTS with the equivalent observable behavior (note: action hiding is not directly assessable in this course) COMP2310 Lecture 4: Concurrent Execution (I)

17 Summary concepts: concurrent processes and process interaction models: asynchronous (arbitrary speed) & interleaving (arbitrary order) parallel composition as a finite state process with action interleaving a (parallel) composite process is equivalent to a (serial) interleaving of its component (serial) processes algebraic laws to express this process interaction by shared actions this forms a primitive for process synchronization (powerful!) and also for process communication (Q: how can they transfer data?) process labeling and action relabeling to control which actions are shared (transform independent actions into shared actions) structure diagrams to visualize these (next lecture) practice: multiple threads in Java (next lecture) COMP2310 Lecture 4: Concurrent Execution (I)