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Blockchain and web3
amm-dex
AMM decentralized exchange
Uniswap
System
Techniques · 8
Primitives · 31
amm-dex
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.
›
Automated market maker
finance · medium: LMSR and constant-product automated market makers that always quote prices from a cost function
Concentrated liquidity
finance · medium: AMM liquidity in price ranges: ticks, sqrt-price math, tick bitmaps, range positions
Reorg safe chain indexing
finance · medium: Index blockchain events with confirmation depth, reorg rollback and finality tracking
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
Congruence closure
compilers · medium: Union-find over terms with congruence propagation; decides equality with uninterpreted functions
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.
›
Reentrancy protection
finance · low: Checks-effects-interactions and reentrancy locks against callback attacks in contracts
Twap oracle
finance · low: Cumulative price accumulators giving manipulation-resistant time-weighted average prices
Big integer arithmetic
numerics · low: Multi-limb integer arithmetic (256-bit and up): carries, Karatsuba, Montgomery and Barrett reduction
Instruction metering
compilers · low: Charge a fuel budget per instruction or per basic block and trap at zero, so untrusted code is bounded by work done, deterministically.
›
Deterministic fixed-point math
game-networking · low: Bit-identical simulation math across CPUs, compilers and builds: integer fixed-point formats, the float traps (FMA, x87, fast-math, libm), deterministic trig, sqrt and RNG.
›
Bellman ford negative cycles
graphs · low: Bellman-Ford shortest paths with negative edges and negative-cycle (arbitrage) detection
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.
›
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.
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
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Rank/select bitvectors
data-structures · low: Bitvector plus small count tables: ones before position i and position of the k-th one in O(1); Elias-Fano builds compressed sorted lists on it.
›
Message sequence numbers
distributed · low: A per-stream counter on every message lets the receiver detect loss, duplicates and reordering, ack cheaply and resume after reconnect with "send from N".
›
Idempotency keys
finance · low: Client-chosen unique key per logical operation, stored with a request fingerprint and the final response, so retries replay the first result instead of acting twice.
›
Journaled state revert
storage · low: Undo journal of state writes enabling nested checkpoints and cheap revert
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
+ 1 more techniques
+ 15 more primitives
System
Techniques · 8
Primitives · 31
amm-dex
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.
›
Automated market maker
finance · medium: LMSR and constant-product automated market makers that always quote prices from a cost function
Concentrated liquidity
finance · medium: AMM liquidity in price ranges: ticks, sqrt-price math, tick bitmaps, range positions
Reorg safe chain indexing
finance · medium: Index blockchain events with confirmation depth, reorg rollback and finality tracking
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
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.
›
Reentrancy protection
finance · low: Checks-effects-interactions and reentrancy locks against callback attacks in contracts
Twap oracle
finance · low: Cumulative price accumulators giving manipulation-resistant time-weighted average prices
Big integer arithmetic
numerics · low: Multi-limb integer arithmetic (256-bit and up): carries, Karatsuba, Montgomery and Barrett reduction
Instruction metering
compilers · low: Charge a fuel budget per instruction or per basic block and trap at zero, so untrusted code is bounded by work done, deterministically.
›
Deterministic fixed-point math
game-networking · low: Bit-identical simulation math across CPUs, compilers and builds: integer fixed-point formats, the float traps (FMA, x87, fast-math, libm), deterministic trig, sqrt and RNG.
›
Bellman ford negative cycles
graphs · low: Bellman-Ford shortest paths with negative edges and negative-cycle (arbitrage) detection
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.
›
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.
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Rank/select bitvectors
data-structures · low: Bitvector plus small count tables: ones before position i and position of the k-th one in O(1); Elias-Fano builds compressed sorted lists on it.
›
Message sequence numbers
distributed · low: A per-stream counter on every message lets the receiver detect loss, duplicates and reordering, ack cheaply and resume after reconnect with "send from N".
›
Idempotency keys
finance · low: Client-chosen unique key per logical operation, stored with a request fingerprint and the final response, so retries replay the first result instead of acting twice.
›
Journaled state revert
storage · low: Undo journal of state writes enabling nested checkpoints and cheap revert
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.
›
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
Fencing tokens
distributed · low: A number that grows with every lock grant and is checked by the protected resource, so a paused ex-holder's late write is rejected.
›
Leases
distributed · low: A lock that expires on its own: bounded-time ownership that survives crashes and partitions, given bounded clock drift and fencing tokens on writes.
›
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).
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
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.
›
Cryptographic hashes (SHA-2, BLAKE3)
security · low: Collision-resistant fingerprints of data; SHA-256 for interoperability, BLAKE3 for speed, HMAC/HKDF for keyed uses.
›
Exponential backoff with jitter
systems · low: Retry after delays that grow geometrically and are randomized, so failed clients spread out instead of hammering a recovering service in synchronized waves.
›
Copy for AI