# Parsers timeline

## Algorithms

List of algorithms (based on this page ↗):

- CYK: Cocke–Younger–Kasami
- bottom-up, Dynamic programming, chart parser
- supports any context-free grammar in Chomsky Normal Form
- $O(n^3)$

- Earley
- Dynamic programming, chart parser
- supports any context-free grammar
- $O(n^3)$

### LL

left-to-right, leftmost derivation (top-down), “recursive descent”

- LL(k)
`k`

tokens of lookahead- very expensive (when introduced)

- LL(1)
- exactly one token lookahead
- much more efficient
- uses
`FIRST()`

and`FOLLOW()`

to build parse tables

- Efficient LL(k)
`k`

tokens of lookahead`k`

is gradually increased w/ backtracking as a fallback- basis of original
`ANTLR`

- GLL: Generalised LL
`LL`

analogue to`GLR`

- maintains multiple parsing descriptors on a stack

- LL(*)
`LL`

analogue to`LAR(m)`

- regular lookaheads w/ cyclic DFAs
- basis of
`ANTLR 3`

- ALL(*): Adaptive LL(*)
- parallel regular lookaheads
- dynamic; adapts to input sentences
- simulates augmented recursive transition networks (ATNs)
- basis of
`ANTLR 4`

- LLLR: a Combination of LL and LR

### LR

left-to-right, rightmost derivation (“bottom-up”), “shift/reduce”

- LR(k)
- allows duplicated states
- fewer conflicts; much larger parse tables

- SLR: Simple LR
- simple
`LR`

:`LR(0)`

states and their transitions `FOLLOW()`

used to compute lookaheads

- simple
- LALR
- similar to
`SLR`

but w/ smaller lookaheads - equivalently, a simplified version of canonical
`LR`

- more complicated lookahead calculation
- basis of yacc/bison

- similar to
- GLR: Generalised LR(k)
- generalized
`LR(k)`

: returns all valid parses - spawns parallel parsing processes on conflicts
- graph-structured stack (
`GSS`

) - more efficient than Earley

- generalized
- LAR(m)
- regular lookaheads w/ cyclic DFAs

- GLR*
- SGLR: Scannerless GLR
- RIGLR: Reduction Incorporated GLR
- RNGLR: Right nulled GLR
- BRNGLR: Binary Right Nulled GLR
- IGLR: Incremental GLR
- MSGLR: Modular SGLR
- ISGLR: Incremental Scannerless GLR

### PEG

- PEG: parsing expression grammar
- similar to CFG-based grammars, but alternation is inherently ordered
- often implemented with “packrat” parsers that memoize partial results
- recursive descent with backtracking

- PEGLL: PEG + GLL