Bit-Level Invariants for Word-Level Constraint Solvers
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Solution Overview
Problem
Existing word-level constraint solvers face performance issues, often timing out when solving complex constraints, due to inefficient backtracking and computation-intensive implication processes, which hinders their ability to find value assignments within a reasonable time frame.
Innovation Solution
The approach involves identifying a proper subset of constraints, applying BDD learning to determine bit-level invariants, and adding these invariants to the original constraints to create a new set that can be solved using a word-level solver, leveraging techniques like BDD learning, forbidden invariants, conditional invariants, and handling duplicate constraints to enhance efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a word-level constraint solver uses extensive backtracking and implication processes to solve complex constraints, then the solver can find value assignments that satisfy all constraints, but the solving time becomes excessively long and the computation becomes too intensive
Solution Approach 1:
The patent applies BDD learning to generate bit-level invariants before the word-level constraint solving process begins. These pre-computed invariants capture essential relationships between bits that would otherwise require extensive backtracking to discover. By performing this learning action in advance, the solver avoids redundant computation during the actual constraint solving, directly reducing solving time while maintaining constraint satisfaction reliability.
Solution Approach 2:
The patent introduces bit-level invariants as an intermediary representation between the original word-level constraints and the constraint solving process. These invariants serve as a bridge that translates complex word-level constraints into simpler bit-level relationships that can be efficiently processed. This intermediary layer allows the solver to work with pre-processed constraint information, reducing the computational burden during backtracking while ensuring all original constraints are satisfied.
2Reliability
If a word-level constraint solver processes all constraints using the implication engine, then the solver ensures all constraints are satisfied, but the computation becomes too intensive and timing out occurs
Solution Approach 1:
The patent segments the constraint processing into two distinct phases: (1) BDD learning phase that generates bit-level invariants from a subset of constraints, and (2) word-level solving phase that uses these invariants to satisfy all constraints. This segmentation allows the computationally intensive BDD learning to be performed once on a subset, rather than repeatedly on all constraints during backtracking. The generated invariants then guide the simpler word-level solving process, reducing overall computation intensity while maintaining reliability.
Solution Approach 2:
The patent applies BDD learning to a proper subset of constraints rather than all constraints. This partial action is sufficient to generate the essential bit-level invariants needed for efficient solving, avoiding the excessive computation that would result from applying BDD learning to the entire constraint set. The generated invariants from the subset are strong enough to guide the solver through satisfying all constraints without requiring full constraint processing at the bit-level.
Data Source
AI summary
Techniques and systems for solving a set of constraints are described. Binary decision diagram (BDD) learning can be applied to a proper subset of the first set of constraints to obtain a set of bit-level invariants. The set of bit-level invariants can then be used for solving the set of constraints. The set of bit-level invariants can include (1) forbidden invariants, (2) conditional invariants, and/or (3) bit-level invariants that are determined by applying BDD learning to a conjunction of constraints and range expressions. If multiple implied constraints have a common right-hand-side (RHS) expression, then BDD learning can be applied to the common RHS expression only once.