Inferring Invariants with Quantifier Alternations: Taming the Search Space Explosion

12/10/2021
by   Jason R. Koenig, et al.
0

We present a PDR/IC3 algorithm for finding inductive invariants with quantifier alternations. We tackle scalability issues that arise due to the large search space of quantified invariants by combining a breadth-first search strategy and a new syntactic form for quantifier-free bodies. The breadth-first strategy prevents inductive generalization from getting stuck in regions of the search space that are expensive to search and focuses instead on lemmas that are easy to discover. The new syntactic form is well-suited to lemmas with quantifier alternations by allowing both limited conjunction and disjunction in the quantifier-free body, while carefully controlling the size of the search space. Combining the breadth-first strategy with the new syntactic form results in useful inductive bias by prioritizing lemmas according to: (i) well-defined syntactic metrics for simple quantifier structures and quantifier-free bodies, and (ii) the empirically useful heuristic of preferring lemmas that are fast to discover. On a benchmark suite of primarily distributed protocols and complex Paxos variants, we demonstrate that our algorithm can solve more of the most complicated examples than state-of-the-art techniques.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/01/2023

Genetic Algorithms for Searching a Matrix of Metagrammars for Synthesis

Syntax-guided synthesis is a paradigm in program synthesis in which the ...
research
05/22/2023

Further Decimating the Inductive Programming Search Space with Instruction Digrams

Overlapping instruction subsets derived from human originated code have ...
research
02/10/2023

Shrinking the Inductive Programming Search Space with Instruction Subsets

Inductive programming frequently relies on some form of search in order ...
research
05/12/2022

Plain and Simple Inductive Invariant Inference for Distributed Protocols in TLA+

We present a new technique for automatically inferring inductive invaria...
research
12/03/2018

Undecidability of Inferring Linear Integer Invariants

We show that the problem of determining the existence of an inductive in...
research
01/27/2020

Layered Clause Selection for Theory Reasoning

Explicit theory axioms are added by a saturation-based theorem prover as...
research
03/27/2021

On Symmetry and Quantification: A New Approach to Verify Distributed Protocols

Proving that an unbounded distributed protocol satisfies a given safety ...

Please sign up or login with your details

Forgot password? Click here to reset