A Pushdown Automaton (PDA) extends a Finite State Machine by adding a stack as auxiliary memory. This extra storage allows PDAs to recognize context-free languages that simple FSMs cannot handle. A classic example is the language aⁿBⁿ — strings consisting of exactly n copies of ‘a’ followed by n copies of ‘b’, for any n ≥ 1. The PDA pushes an ‘a’ onto the stack for every ‘a’ it reads, then pops one entry for every ‘b’. If the stack is empty exactly when all input is consumed, the string is accepted.
Continue reading Push Down Automata in Java for Equal Number of a’s and b’sIllustrating Epsilon Closure in Java
In the theory of computation, epsilon-closure (ε-closure) is a fundamental operation for converting a Non-deterministic Finite Automaton (NFA) with ε-transitions into an equivalent Deterministic Finite Automaton (DFA). The ε-closure of a state s is the set of all states reachable from s by following zero or more ε-transitions alone, without consuming any input symbol. In this post, we implement ε-closure computation in Java using a recursive depth-first approach.
Continue reading Illustrating Epsilon Closure in JavaFinite State Machine: Implementing Binary Adder in Java
A Finite State Machine (FSM) is a mathematical model of computation that transitions between a finite set of states based on input. One elegant application is a binary adder — where two binary strings are added bit-by-bit from right to left, with the FSM managing carry propagation between two states: no-carry (state 0) and carry (state 1). In this post, we implement this FSM-based binary adder in Java, complete with state transition functions and step-by-step output.
Continue reading Finite State Machine: Implementing Binary Adder in JavaMultithreading Example in Java
In this post, we implement a basic Multithreading example in Java. Multithreading allows multiple threads to execute concurrently within a single program, enabling tasks to run in parallel rather than one after another. Java has built-in support for multithreading through the Thread class and the Runnable interface.
What is Multithreading?
A thread is the smallest unit of execution within a process. When a program creates multiple threads, the operating system’s thread scheduler interleaves their execution — giving each thread a slice of CPU time in turn. This makes it appear as though they are running simultaneously (and on multi-core systems, they actually can be).
In this example, we create two threads by extending the Thread class and overriding its run() method. Each thread prints a label 4 times, pausing 500 ms between prints. Both threads run concurrently, so their output interleaves.
start()— Tells the JVM to create a new OS-level thread and invokerun()on it. Callingrun()directly would execute it on the current thread, not a new one.Thread.sleep(ms)— Pauses the current thread for the given number of milliseconds, allowing other threads to execute.InterruptedException— Must be caught when callingsleep(). It fires if another thread interrupts this one while it is sleeping.
Illustrating Working of FIFO Page Replacement Algorithm in C++
In this post, we implement the FIFO (First In, First Out) Page Replacement Algorithm in C++. When the OS needs to load a new page into memory but all frames are occupied, FIFO evicts the page that has been in memory the longest — the one that arrived first. It is one of the simplest page replacement strategies and serves as a baseline for comparing more sophisticated algorithms.
What is FIFO Page Replacement?
Physical memory is divided into frames. When a process references a page not currently in a frame (a page fault), it must be loaded. If all frames are full, an existing page must be evicted. FIFO chooses the oldest resident page for eviction, regardless of how frequently it has been used.
- Page Hit — Referenced page is already in a frame. No disk I/O needed.
- Page Fault (Miss) — Referenced page is not in any frame. Must load from disk.
- FIFO Queue — Tracks the order in which pages were loaded. Front = oldest; back = newest.
A notable weakness of FIFO is Bélady’s Anomaly — adding more frames can sometimes cause more page faults, counter-intuitively.
Continue reading Illustrating Working of FIFO Page Replacement Algorithm in C++Implementing Banker’s Algorithm in C++
In this post, we implement the Banker’s Algorithm in C++ — a classic deadlock avoidance mechanism in operating systems proposed by Edsger Dijkstra. The algorithm is named after the analogy of a bank that never lends money in a way that could prevent it from satisfying all customers’ future needs.
What is the Banker’s Algorithm?
Before granting any resource request, the OS runs the Banker’s Algorithm to check whether doing so keeps the system in a safe state. A safe state is one where a safe sequence exists — an ordering of all processes such that each can eventually complete using currently available resources plus the resources released by earlier processes in the sequence.
If no safe sequence exists, the state is unsafe, meaning deadlock is possible. The OS denies the request in that case.
Three data structures are needed:
- Available[] — Current free units of each resource type.
- Allocated[][] — Resources currently held by each process.
- Maximum[][] — The maximum resources each process may ever request.
- Need[][] — Remaining resources a process may still request:
Need[i][j] = Maximum[i][j] - Allocated[i][j]
Implementing SJF (Shortest Job First) Scheduling Algorithm in C++
In this post, we implement the Shortest Job First (SJF) CPU scheduling algorithm in C++. SJF always selects the process with the smallest burst time from the ready queue and executes it next. This greedy approach provably minimizes the average waiting time, making SJF theoretically optimal among all non-preemptive algorithms when all jobs are available simultaneously.
What is SJF Scheduling?
In SJF, the scheduler sorts all ready processes by their burst (execution) time in ascending order and then runs them in that sequence. The shortest job finishes earliest, releasing the CPU quickly for others and keeping the average wait low.
It is non-preemptive — once started, a process runs to completion. The preemptive variant is called Shortest Remaining Time First (SRTF).
- Waiting Time (WT):
WT[i] = WT[i-1] + BurstTime[i-1] - (ArrivalTime[i] - ArrivalTime[i-1]) - Turnaround Time (TT):
TT[i] = WT[i] + BurstTime[i]
The key risk with SJF is starvation: if short jobs keep arriving, long jobs may never execute.
Continue reading Implementing SJF (Shortest Job First) Scheduling Algorithm in C++