diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 5c3ef77..f0a2189 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -4,21 +4,20 @@ "type": "split", "children": [ { - "id": "32947c2821d23646", + "id": "65ffc94caaa1d4a8", "type": "tabs", "children": [ { - "id": "7c5b0ca6f7687800", + "id": "eb9b42e21c969fd9", "type": "leaf", "state": { - "type": "markdown", + "type": "diff-view", "state": { - "file": "Concurrent Systems/notes/2b - Round Robin algorithm.md", - "mode": "source", - "source": false + "file": "Concurrent Systems/notes/6 - Atomicity.md", + "staged": false }, - "icon": "lucide-file", - "title": "2b - Round Robin algorithm" + "icon": "git-pull-request", + "title": "Diff View (6 - Atomicity)" } } ] @@ -189,14 +188,16 @@ "companion:Toggle completion": false } }, - "active": "7c5b0ca6f7687800", + "active": "eb9b42e21c969fd9", "lastOpenFiles": [ "Concurrent Systems/notes/1b - Peterson algorithm.md", + "Concurrent Systems/notes/2b - Round Robin algorithm.md", + "Concurrent Systems/notes/10 - Implementing Consensus.md", + "\u0001.md", "Concurrent Systems/notes/images/Pasted image 20250405000438.png", "Pasted image 20250405000428.png", "Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md", "Concurrent Systems/notes/4 - Semaphores.md", - "Concurrent Systems/notes/2b - Round Robin algorithm.md", "Concurrent Systems/notes/4b - Monitors.md", "Concurrent Systems/notes/4c - Dining Philosophers.md", "Concurrent Systems/a.md", @@ -204,7 +205,6 @@ "Concurrent Systems/notes/images/Pasted image 20250304093223.png", "Concurrent Systems/notes/Untitled.md", "Concurrent Systems/notes/9 - Consensus.md", - "Concurrent Systems/notes/10 - Implementing Consensus.md", "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md", "Concurrent Systems/notes/7- MUTEX-free concurrency.md", "Concurrent Systems/notes/6 - Atomicity.md", diff --git a/Concurrent Systems/notes/1 - CS Basics.md b/Concurrent Systems/notes/1 - CS Basics.md index 7142d24..2966036 100644 --- a/Concurrent Systems/notes/1 - CS Basics.md +++ b/Concurrent Systems/notes/1 - CS Basics.md @@ -62,7 +62,7 @@ function withdraw() { While `read()` and `write()` may be considered as atomic, their sequential composition **is not**. -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250303090135.png) +![](images/Pasted%20image%2020250303090135.png) #### Mutual Exclusion (MUTEX) Ensure that some parts of the code are executed as *atomic*. @@ -100,7 +100,7 @@ Every solution to a problem should satisfy at least: **Both inclusions are strict:** $$\text{Deadlock freedom} \not \implies \text{Starvation freedom}$$ - ![](Concurrent%20Systems/notes/images/Pasted%20image%2020250303093116.png) + ![](images/Pasted%20image%2020250303093116.png) *p1 is starving!* $$\text{Starvation freedom} \not \implies \text{Bounded bypass}$$ Assume a $f$ and consider the scheduling above, where p2 wins $f(3)$ times and so does p3, then p1 looses (at least) $2f(3)$ times before winning. diff --git a/Concurrent Systems/notes/10 - Implementing Consensus.md b/Concurrent Systems/notes/10 - Implementing Consensus.md index 2e3765a..d2acac1 100644 --- a/Concurrent Systems/notes/10 - Implementing Consensus.md +++ b/Concurrent Systems/notes/10 - Implementing Consensus.md @@ -30,7 +30,7 @@ A configuration C obtained during the execution of all A is called: If A wait-free implements binary consensus for n processes, then there exists a bivalent initial configuration. *Proof:* -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250401083747.png) +![](images/Pasted%20image%2020250401083747.png) ### CN(Atomic R/W registers) = 1 **Thm:** There exists no wait-free implementation of binary consensus for 2 processes that uses atomic R/W registers. @@ -135,7 +135,7 @@ propose(i, v) := Let us consider a verison of the compare&swap where, instead of returning a boolean, it always returns the previous value of the object, i.e.: -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250401092557.png) +![](images/Pasted%20image%2020250401092557.png) ``` CS a compare&swap object init at ⊥ diff --git a/Concurrent Systems/notes/1b - Peterson algorithm.md b/Concurrent Systems/notes/1b - Peterson algorithm.md index 425ef18..cd7a728 100644 --- a/Concurrent Systems/notes/1b - Peterson algorithm.md +++ b/Concurrent Systems/notes/1b - Peterson algorithm.md @@ -56,7 +56,7 @@ a) `FLAG[1] = down`, this is possible only with the following interleaving: ![](images/Pasted%20image%2020250303100721.png) b) `AFTER_YOU = 1`, this is possible only with the following interleaving: -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250303100953.png) +![](images/Pasted%20image%2020250303100953.png) ##### Bounded Bypass proof (with bound = 1) - If the wait condition is true, then it wins (and waits 0). diff --git a/Concurrent Systems/notes/2 - Fast mutex by Lamport.md b/Concurrent Systems/notes/2 - Fast mutex by Lamport.md index ca60352..efab6df 100644 --- a/Concurrent Systems/notes/2 - Fast mutex by Lamport.md +++ b/Concurrent Systems/notes/2 - Fast mutex by Lamport.md @@ -49,9 +49,9 @@ unlock(i) := ##### MUTEX proof How can pi enter its CS? -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250304084537.png) +![](images/Pasted%20image%2020250304084537.png) -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250304084901.png) +![](images/Pasted%20image%2020250304084901.png) (*must finished before nel senso che $p_i$ deve aspettare $p_j$*) ##### Deadlock freedom Let $p_i$ invoke lock @@ -72,6 +72,6 @@ Let $p_i$ invoke lock - In the second wait Y = ⊥: but then there exists a $p_h$ that eventually enters its CS -> good - In the ∀j.wait FLAG[j]=down: this wait cannot block a process forever -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250304090219.png) +![](images/Pasted%20image%2020250304090219.png) esercizio: prova che NON soddisfa starvation freedom \ No newline at end of file diff --git a/Concurrent Systems/notes/2b - Round Robin algorithm.md b/Concurrent Systems/notes/2b - Round Robin algorithm.md index e1cbc7e..9bab504 100644 --- a/Concurrent Systems/notes/2b - Round Robin algorithm.md +++ b/Concurrent Systems/notes/2b - Round Robin algorithm.md @@ -50,5 +50,5 @@ By Deadlock freedom of RR, at least one process eventually unlocks The worst case is when TURN = *i+1* mod n when FLAG[i] is set. -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250304093223.png) +![](images/Pasted%20image%2020250304093223.png) diff --git a/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md b/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md index d333ed8..f95bec8 100644 --- a/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md +++ b/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md @@ -31,7 +31,7 @@ unlock(i) := *Proof:* by contradiction. Let's consider the execution of $p_i$ leading to its CS: -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250310172134.png) +![](images/Pasted%20image%2020250310172134.png) **Corollary** (of the MUTEX proof)**:** DATE is never written concurrently. @@ -57,7 +57,7 @@ Let's consider the execution of $p_i$ leading to its CS: **Theorem:** the algorithm satisfies bounded bypass with bound $2n-2$. *Proof:* -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250310103703.png) +![](images/Pasted%20image%2020250310103703.png) so by this, the very worst possible case is that my lock experiences that. It looks like I can experience at most $2n-1$ other critical sections, but it is even better, let's see: diff --git a/Concurrent Systems/notes/5 - Software Transactional Memory.md b/Concurrent Systems/notes/5 - Software Transactional Memory.md index 3a00fd3..87a6eea 100644 --- a/Concurrent Systems/notes/5 - Software Transactional Memory.md +++ b/Concurrent Systems/notes/5 - Software Transactional Memory.md @@ -105,7 +105,7 @@ The **casual past** of a transaction T is the set of all T' and T'' such that VWC allows more transactions to commit -> it is a more liberal property than opacity. -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250317105355.png) +![](images/Pasted%20image%2020250317105355.png) #### A Vector clock based STM system We have m shared MRMW registers; register X is represented by a pair XX, with: diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md index 8a00e32..e49118a 100644 --- a/Concurrent Systems/notes/6 - Atomicity.md +++ b/Concurrent Systems/notes/6 - Atomicity.md @@ -21,9 +21,9 @@ A complete history $\hat{H}$ is **linearizable** if there exists a sequential hi Given an history $\hat{K}$, we can define a binary relation on events $⟶_{K}$ s.t. (op, op’) ∈ ⟶K if and only if res[op] _{proc} op'$ to hold whenever there exists a process p that ### Sequential consistency **Def:** a complete history is sequentially consistent if there exists a sequential history $𝑆$ s.t. -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250324082534.png) +![](images/Pasted%20image%2020250324082534.png) -![](Concurrent%20Systems/notes/images/Pasted%20image%2020250324082545.png) +![](images/Pasted%20image%2020250324082545.png) >[!warning] >The problem with sequential consistency is that it is NOT compositional. diff --git a/Concurrent Systems/notes/7- MUTEX-free concurrency.md b/Concurrent Systems/notes/7- MUTEX-free concurrency.md index e4a40dc..2280835 100644 --- a/Concurrent Systems/notes/7- MUTEX-free concurrency.md +++ b/Concurrent Systems/notes/7- MUTEX-free concurrency.md @@ -64,7 +64,7 @@ this implementation satisfies the three requirements for the splitter - let us consider the last process that writes into LAST (this is an atomic register, so this is meaningful) - if the door is closed, it receives R and √ 3. let $p_i$ be the first process that receives $S \to LAST=i$ in its second if - ![](Concurrent%20Systems/notes/images/Pasted%20image%2020250324091452.png) + ![](images/Pasted%20image%2020250324091452.png) ### An Obstruction-free Timestamp Generator A **timestamp generator** is a concurrent object that provides a single operation get_ts such that: @@ -98,7 +98,7 @@ this implementation satisfies the three properties of the timestamp generator - every process that starts after its termination will find NEXT to a greater value (NEXT never decreases!) 3. Obstruction freedom is trivial -**REMARK:** this implementation doesn’t satisfy the non-blocking property:![](Concurrent%20Systems/notes/images/Pasted%20image%2020250324092633.png) +**REMARK:** this implementation doesn’t satisfy the non-blocking property:![](images/Pasted%20image%2020250324092633.png) ### A Wait-free Stack REG is an unbounded array of atomic registers (the stack) @@ -149,7 +149,7 @@ This is needed for the so called ABA problem with compare&set: - with the compare&set you mainly test that the sequence_number has not changed TOP : a register that can be read or compare&setted - ![](Concurrent%20Systems/notes/images/Pasted%20image%2020250324100652.png) + ![](images/Pasted%20image%2020250324100652.png) ``` push(w) :=