Context-Free Language Reachability

Introduction

The CFL module (arlib/cfl) implements algorithms for context-free language (CFL) reachability analysis, a powerful framework for program analysis problems including points-to analysis, interprocedural dataflow analysis, and shape analysis.

Key Features

  • CFL-Reachability Algorithms: Classical and quantum-inspired dynamic transitive closure

  • Dyck Language Support: Balanced-parenthesis reachability for call-return matching

  • Graph-Based Analysis: Efficient graph algorithms for program analysis

  • Matrix-Based Computation: Matrix formulations for parallel processing

  • Strong Component Reduction: Optimization via strongly connected components

Components

CFL Solvers (arlib/cfl/cfl_solver.py)

Core CFL-reachability solving:

from arlib.cfl import CFLSolver

# Create solver for CFL-reachability
solver = CFLSolver()

# Define grammar and graph
grammar = load_grammar("grammar.txt")
graph = load_graph("program_graph.dot")

# Compute reachability
reachable = solver.solve(grammar, graph)

Dynamic Transitive Closure (arlib/cfl/cfl_dtc.py, arlib/cfl/dtc.py)

Dynamic transitive closure algorithms including quantum-inspired methods:

from arlib.cfl.cfl_dtc import QuantumDTC

# Quantum-inspired dynamic transitive closure
dtc = QuantumDTC()
closure = dtc.compute(graph)

Grammar Support (arlib/cfl/grammar.py)

Context-free grammar manipulation:

  • Grammar parsing and validation

  • Production rule management

  • Dyck language generation

  • Grammar normalization

Matrix-Based Algorithms (arlib/cfl/matrix.py, arlib/cfl/pag_matrix.py)

Matrix formulations for efficient CFL-reachability:

from arlib.cfl.pag_matrix import PAGMatrix

# Program assignment graph as matrix
pag = PAGMatrix(graph)
result = pag.cfl_reachability(grammar)

Strong Component Reduction (arlib/cfl/sc_solver.py)

Optimization using strongly connected components:

from arlib.cfl.sc_solver import SCReducer

# Reduce problem via SCC decomposition
reducer = SCReducer()
reduced_result = reducer.solve(graph, grammar)

Applications

  • Points-To Analysis: Field-sensitive and context-sensitive pointer analysis

  • Call Graph Construction: Interprocedural control flow analysis

  • Alias Analysis: May-alias and must-alias analysis

  • Shape Analysis: Heap shape abstraction

  • Taint Analysis: Information flow tracking

  • Interprocedural Dataflow: Summary-based dataflow analysis

References

  • Reps, T. (1998). Program Analysis via Graph Reachability. Information and Software Technology

  • Yannakakis, M. (1990). Graph-Theoretic Methods in Database Theory. PODS 1990

  • Zhang, Q., Su, Z. (2017). Context-Sensitive Data-Dependence Analysis via Linear Conjunctive Language Reachability. POPL 2017

  • Liu, J., et al. (2024). Dynamic Transitive Closure-Based Static Analysis through the Lens of Quantum Search. TOSEM 2024