Theorem Proving Sampling With Dynamic Step Size Limits
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Solution Overview
Problem
Existing automated theorem proving methods face inefficiencies due to unbounded sampling step sizes, leading to longer action sequences and incorrect solutions, and other approaches like iterative deepening and random restarting have undesirable drawbacks.
Innovation Solution
A method that initializes a sampling step size, performs sampling within this limit, checks for solution, and increases the step size if the problem is not solved, with a constant value to manage the sampling process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If unbounded sampling step size is used, then the search space is fully explored, but the action sequence becomes longer and computational overhead increases
Solution Approach 1:
The sampling step size is made dynamic rather than fixed or unbounded. The method uses iterative deepening with a maximum depth limit that can be adjusted, allowing the search to adapt its depth based on problem complexity while preventing excessive computational overhead from unbounded exploration
Solution Approach 2:
The sampling step size parameter is changed from unbounded to bounded with a maximum depth limit. This parameter modification allows the system to balance thorough search space exploration with computational efficiency by stopping sampling when the depth limit is reached
2Productivity
If fixed sampling step size is used, then computational overhead is reduced, but solution accuracy decreases due to premature termination
Solution Approach 1:
The sampling step size transitions from fixed to dynamic through iterative deepening. The method starts with a lower depth limit and progressively increases it, allowing the system to achieve both computational efficiency at lower depths and solution accuracy at higher depths as needed
Solution Approach 2:
The sampling process uses periodic iterative deepening cycles where the depth limit is increased after unsuccessful attempts at lower depths. This periodic adjustment of the sampling step size allows the system to maintain efficiency while progressively improving accuracy
3Reliability
If iterative deepening is used, then solution accuracy improves, but device complexity increases
Solution Approach 1:
The iterative deepening mechanism is self-managing and automatically adjusts the sampling step size based on whether the problem is solved at each depth level. The system autonomously determines when to increase depth without external intervention, reducing the need for complex external control mechanisms
Data Source
AI summary
Examples described herein provide a computer-implemented method that includes setting a sampling step size and a constant value as parameters to solve a theorem proving problem. The method further includes performing a first sampling step starting with an initial state of the theorem proving problem and limited by the sampling step size. The method further includes determining whether the theorem proving problem is solved. The method further includes, responsive to determining that the theorem proving problem is not solved, increasing the sampling step size based on the constant value to define an increased sampling step size. The method further includes performing a second sampling step limited by the increased sampling step size.