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Transport, logistics and mobility
rail-signalling
rail signalling
ETCS, CBTC
System
Techniques · 14
Primitives · 48
rail-signalling
Clock synchronization
distributed · medium: Estimate a clock's offset from four timestamps, filter out queueing noise, and steer the clock smoothly; NTP gets about a millisecond, PTP with hardware timestamps under a microsecond.
›
Fault tree analysis
embedded · medium: Write the unwanted top event as AND/OR logic over component failures, reduce it to minimal cut sets, then compute its probability and each failure's share.
›
Model checking and formal proof
embedded · medium: Exhaustively explore a model's reachable states (or prove its invariants with a solver or proof assistant) to find rule violations with a shortest counterexample trace.
›
Interlocking logic
embedded · medium: Railway route setting, locking, flank protection and release as verified boolean logic
Movement authority braking curves
embedded · medium: Train supervision: compute braking curves from movement authority and enforce speed limits
Safety-critical coding standards
embedded · medium: Which rule sets (MISRA C, CERT C, JPL Power of Ten, Rust lint subsets) apply when software must not fail, what they forbid, and how to enforce them in CI.
›
Safety monitor architecture
embedded · medium: Independent doer/checker safety monitor that forces a safe state when the main channel misbehaves
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
Redundancy voting
embedded · low: N-modular redundancy and MooN voting (2oo3, TMR) with discrepancy detection
End to end protection e2e
embedded · low: Per-message counter, ID and CRC over a black channel to detect loss, repetition, corruption, delay
Watchdog timer
embedded · low: A hardware down-counter that resets the chip unless software proves, in time and in a plausible pattern, that it is still healthy.
›
Time triggered scheduling
embedded · low: Static cyclic schedules where every task and message has a precomputed time slot
Kalman filter
robotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.
›
Message authentication codes (HMAC,…
security · low: A keyed short tag proving a message is unmodified and came from a key holder; pick HMAC, CMAC, KMAC or a one-time polynomial MAC by what primitive you already have.
›
Hierarchical state machine
systems · low: Nest states so a substate inherits its parent's reactions and only overrides what differs, with ordered entry and exit actions along the path.
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PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
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Phase-locked loop (digital)
signal-processing · low: Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
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Binary decision diagrams
optimization · low: A reduced ordered BDD stores a Boolean function as a shared DAG that is unique per variable order, so equivalence is one integer compare and counting is one pass.
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Swiss table
data-structures · low: Open-addressing hash table that filters 8-16 slots at once with 1-byte hash tags and SIMD, giving fast lookups at 87.5 % load.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Velocity motion profiles
robotics · low: Trapezoidal and S-curve (jerk-limited) velocity profiles for point-to-point moves
+ 7 more techniques
+ 32 more primitives
System
Techniques · 14
Primitives · 48
rail-signalling
Clock synchronization
distributed · medium: Estimate a clock's offset from four timestamps, filter out queueing noise, and steer the clock smoothly; NTP gets about a millisecond, PTP with hardware timestamps under a microsecond.
›
Fault tree analysis
embedded · medium: Write the unwanted top event as AND/OR logic over component failures, reduce it to minimal cut sets, then compute its probability and each failure's share.
›
Model checking and formal proof
embedded · medium: Exhaustively explore a model's reachable states (or prove its invariants with a solver or proof assistant) to find rule violations with a shortest counterexample trace.
›
Interlocking logic
embedded · medium: Railway route setting, locking, flank protection and release as verified boolean logic
Movement authority braking curves
embedded · medium: Train supervision: compute braking curves from movement authority and enforce speed limits
Safety-critical coding standards
embedded · medium: Which rule sets (MISRA C, CERT C, JPL Power of Ten, Rust lint subsets) apply when software must not fail, what they forbid, and how to enforce them in CI.
›
Safety monitor architecture
embedded · medium: Independent doer/checker safety monitor that forces a safe state when the main channel misbehaves
Sensor fusion
robotics · medium: Combining IMU, GNSS, camera, lidar and radar estimates with Kalman-type filters and time alignment
Dataflow analysis
compilers · medium: Compute a fact per program point (live variables, reaching definitions, available expressions) by iterating transfer functions over the CFG to a fixed point.
›
CDCL SAT solving
optimization · medium: Search for a satisfying assignment, learn a new constraint from every dead end, and jump back past irrelevant choices; handles industrial formulas with millions of clauses.
›
Dpll t
optimization · medium: SMT architecture: CDCL over boolean abstraction plus theory solvers, theory propagation, Nelson-Oppen
Transform tree
robotics · medium: Time-indexed tree of coordinate frames with interpolated lookups between any two frames
Congruence closure
compilers · medium: Union-find over terms with congruence propagation; decides equality with uninterpreted functions
Bit blasting
optimization · medium: Reduce bit-vector constraints to CNF via adder, multiplier and comparator circuits
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
Redundancy voting
embedded · low: N-modular redundancy and MooN voting (2oo3, TMR) with discrepancy detection
End to end protection e2e
embedded · low: Per-message counter, ID and CRC over a black channel to detect loss, repetition, corruption, delay
Watchdog timer
embedded · low: A hardware down-counter that resets the chip unless software proves, in time and in a plausible pattern, that it is still healthy.
›
Time triggered scheduling
embedded · low: Static cyclic schedules where every task and message has a precomputed time slot
Kalman filter
robotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.
›
Message authentication codes (HMAC,…
security · low: A keyed short tag proving a message is unmodified and came from a key holder; pick HMAC, CMAC, KMAC or a one-time polynomial MAC by what primitive you already have.
›
Hierarchical state machine
systems · low: Nest states so a substate inherits its parent's reactions and only overrides what differs, with ordered entry and exit actions along the path.
›
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
›
Phase-locked loop (digital)
signal-processing · low: Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
Binary decision diagrams
optimization · low: A reduced ordered BDD stores a Boolean function as a shared DAG that is unique per variable order, so equivalence is one integer compare and counting is one pass.
›
Swiss table
data-structures · low: Open-addressing hash table that filters 8-16 slots at once with 1-byte hash tags and SIMD, giving fast lookups at 87.5 % load.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Velocity motion profiles
robotics · low: Trapezoidal and S-curve (jerk-limited) velocity profiles for point-to-point moves
Code coverage instrumentation
compilers · low: Insert counters into compiled code to record which blocks, edges or lines ran; a spanning tree of the control-flow graph cuts the counters needed.
›
Memory protection unit
embedded · low: A handful of base/size regions with permissions, checked on every access by the CPU, give microcontroller tasks isolation and stack-overflow traps without an MMU.
›
SPSC ring buffer
data-structures · low: Bounded wait-free queue for exactly one producer and one consumer thread, built from an array and two indices with acquire/release ordering.
›
Complementary filter
robotics · low: Blend high-passed gyro integration with low-passed accelerometer/magnetometer attitude (Mahony/Madgwick)
Extended Kalman filter
robotics · low: Kalman filter for nonlinear motion and measurement models: linearize f and h with Jacobians at the current estimate each step. The default estimator in robot navigation.
›
Control-flow graph
compilers · low: Split a linear instruction list into basic blocks and connect them by jumps; the graph every optimizer, SSA builder and dataflow pass walks.
›
Topological sort
graphs · low: Order the vertices of a DAG so every edge points forward; the core of build systems, schedulers and dependency resolution, with cycle detection for free.
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
Drat proof certificates
optimization · low: DRAT and LRAT proofs emitted by SAT solvers and checked independently
Two watched literals
optimization · low: Unit propagation for SAT that watches just two literals per clause, so backtracking costs nothing and long clauses are rarely touched.
›
Arena allocator
systems · low: Allocate by bumping a pointer through big chunks and free everything at once: a few instructions per allocation for objects sharing a lifetime.
›
Simplex method
optimization · low: Solves linear programs by walking along the edges of the feasible polytope from vertex to vertex, one basis swap (pivot) at a time; the workhorse behind MIP solvers.
›
Quaternion rotations
geometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.
›
Lowest common ancestor
graphs · low: LCA/merge-base computation in trees and DAGs
Rigid-body transforms (SE(3) poses)
robotics · low: Represent, compose, invert, integrate and interpolate 3D poses as unit quaternion plus translation, with exp/log maps for small motions and uncertainty.
›
Hash consing
data-structures · low: Intern structurally equal immutable terms so equality is pointer comparison and sharing is maximal
Union-find
graphs · low: Disjoint-set forest with union by size and path compression; merges sets and answers same-set queries in effectively constant time.
›
Arithmetic circuits
hardware-os · low: Adder and multiplier circuits: carry-lookahead, prefix adders, Booth encoding, Wallace and Dadda trees
Tseitin transformation
optimization · low: Linear-size CNF encoding of formulas with auxiliary variables
False sharing
concurrency · low: Independent variables written by different cores on one cache line force the line to bounce between cores; pad or regroup hot data to fix it.
›
Memory ordering
concurrency · low: What Relaxed, Acquire, Release and SeqCst atomics actually guarantee, what they cost on x86 and ARM, and which one each pattern needs.
›
Dma transfers
embedded · low: DMA controllers: descriptors, circular buffers, cache coherence for zero-CPU data movement
PWM generation
embedded · low: A timer's counter, period and compare registers draw the pulse train; preload, dead time and DMA make duty changes glitch-free, shoot-through-free and cheap.
›
Homogeneous transforms
geometry · low: 4x4 affine and projective matrices, homogeneous coordinates, view and projection, normal matrices
Minimum spanning tree
graphs · low: Cheapest set of edges connecting all vertices; Kruskal sorts edges and joins components with union-find, Prim grows one tree, Boruvka merges in parallel rounds.
›
CPU caches and the memory hierarchy
hardware-os · low: Sizes, line widths and latencies of L1/L2/L3/DRAM on modern x86 and Apple M-series, and the data-layout rules that follow from them.
›
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
›
Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
›
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
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