2/23/09 Distributed Shared memory Bertinoro, March 2009 Algorithms Part III 2 • Shared memory distributed system – Set of processes Distributed Algorithms – Set of shared objects (variables) • access to a shared variable is a single (indivisible) event PART III • CommunicaCon through shared variables – No channels SHARED MEMORY • We use a single automaton to model the enCre system – using several automata and the composiCon operaCon leads to some (technical) difficulCes 1 Distributed Shared memory Bertinoro, March 2009 Distributed Shared memory Bertinoro, March 2009 Algorithms Algorithms Part III 3 Part III 4 Port 1 Port 2 Port n • However, we think of each p i as an automaton – states i , start i , … • Each shared variable x – values x , ini0al x , … • binary values, arbitrary values, bounded, unbounded … p n p 1 p 2 – single/mulCple • single‐writer or mulCple‐writer • single‐reader or mulCple‐reader – type (read‐write, read‐modify‐write, …) • The overall system automaton A – states, consists of a state for each p i and a value for each shared variable – start, consists of a start state for each p i and an iniCal value for each shared variable Automaton for the enCre system Distributed Shared memory Bertinoro, March 2009 Distributed Shared memory Bertinoro, March 2009 Algorithms Algorithms Part III 5 Part III 6 • act(A), set of acCons • trans(A) – each acCon is “associated” with a p i – restricted so that only the state of involved process and shared variables can be changed • Some acCons – ( s , π , s ’) is a valid step for A if ( s i , π , s i ’) is a valid step for p i – “associated” also with a (some) shared variable(s) • π cannot change state of other processes – π can access only associated variables • Input/output acCons of p i – “port” of process i • Technicality • Internal acCons of p i – if π associated with p i and with shared variable x , – local computaCon then whether or not π is enabled should depend only on the state of p i and not on x . 1
2/23/09 Distributed Shared memory Bertinoro, March 2009 Distributed Shared memory Bertinoro, March 2009 Algorithms Algorithms Part III 7 Part III 8 SharedVarConsensus automaton • tasks(A) States, for each i : status i ∈ { idle,access,decide,done }, iniCally idle – task structure consistent with process structure input i ∈ V ∪ { ⊥ } , iniCally ⊥ output i ∈ V ∪ { ⊥ } , iniCally ⊥ – each equivalence class should include only acCons Shared variables: associated with a process x ∈ V ∪ { ⊥ } , iniCally ⊥ , accessible by all processes • that is an equivalence class cannot contain acCons of p i Transi=ons, for each i : and acCons of p j . inp init ( v ) i out decide ( v ) i fect: input i := v Pr e: status i = decide Ef Effect: Pre: if status i = idle then output i = v status i := access Ef Effect: fect: status i = done Example int access i e: status i = access Pr Pre: Set of n processes, one shared variable x Ef fect: if x = ⊥ then x := input i Effect: output i := x Consensus problem: status i := decide port i : init i ( v ), decide i ( v ) Tasks: for every i, { access i , decide i } Distributed Shared memory Bertinoro, March 2009 Distributed Shared variables type Bertinoro, March 2009 Algorithms Algorithms Part III 9 Part III 10 • We can model the environment that controls • Variable type each process with an automaton – set V of values – an iniCal value v 0 ∈ V – a set of invoca0ons • For the previous case we can have – a set of responses – Automaton U i that controls init i and receives the – a funcCon f : invoca0ons × V → responses × V decide i acCons – init i executed only once • A variable type is not an automaton • Exercise: write automaton code for U i – Looks similar – Invoca=ons and responses occur together as part of a func=on applica=on Distributed Shared variable types Bertinoro, March 2009 Distributed Shared variable types Bertinoro, March 2009 Algorithms Algorithms Part III 11 Part III 12 • Read/write shared variables (register) • Read‐modify‐write shared variables – invocaCons are: read and write ( v ) – responses are: v (a value), ack – the funcCon f allows to – funcCon: • read the variable • f ( read , v ) =( v , v ) • perform some local computaCon • f ( write ( v ), w )=( ack ,v) • write a new value into the variable • QuesCon – all in one step – The shared variable used in the Consensus example is a read‐write variable? • Difficult to implement • Exercise: rewrite the code of the Consensus example using a read‐write shared variable – two accesses (a read and a write) – Hint instead of one single acCon that reads and writes x you need two acCons (one for reading and another for wriCng) – Can you make it work? Show an example where it fails. 2
2/23/09 Distributed Shared variables type Bertinoro, March 2009 Distributed Shared variables Bertinoro, March 2009 Algorithms Algorithms Part III 13 Part III 14 • Swap f ( u,v )=( v , u ) • Compare‐and‐swap f (( u,v ), w )= ( w , v ), if u = w ( w , w ), otherwise MUTUAL EXCLUSION AND RESUORCE ALLOCATION • Test‐and‐set f ( u,v )=( v ,1) • Fetch‐and‐add f ( u , v )=( v , u+v ) Distributed Mutual Exclusion Bertinoro, March 2009 Distributed Mutual Exclusion Bertinoro, March 2009 Algorithms Algorithms Part III 15 Part III 16 • Resource allocaCon problem – single resource that can support only one‐user at • Each process has 4 regions Remainder a Cme (e.g. a printer) – Remainder – several users U 1 , U 2 , … , U n want to access the – Trying Trying resource – CriCcal – Exit • In an “operaCng systems” sehng CriCcal – several processes have a porCon of their code • ExecuCon loops in these regions which is called “criCcal region” Exit – no two processes can concurrently execute their criCcal regions Distributed Mutual Exclusion Bertinoro, March 2009 Distributed Mutual Exclusion Bertinoro, March 2009 Algorithms Algorithms Part III 17 Part III 18 • User U i issues U 1 U n – try i acCons (request to access the resource) try 1 exit 1 try n exit n – exit i acCons (request to leave the resource) crit 1 rem 1 crit n rem n • Need to output – crit i (to grant the resource) p n p 2 p 1 – rem i (to return to the remainder region) • U i is well‐formed – if it follows the cycle of acCons try i ‐ ( crit i ) – exit i ‐ ( rem i ) 3
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