A Practical Linear Time Algorithm for Trivial Automata Model Checking of Higher-Order Recursion Schemes

Abstract

Abstract. The model checking of higher-order recursion schemes has been actively studied and is now becoming a basis of higher-order program verification. We propose a new algorithm for trivial automata model checking of higher-order recursion schemes. To our knowledge, this is the first practical model checking algorithm for recursion schemes that runs in time linear in the size of the higher-order recursion scheme, under the assumption that the size of trivial automata and the largest order and arity of functions are fixed. The previous linear time algorithm was impractical due to a huge constant factor, and the only practical previous algorithm suffers from the hyper-exponential worst-case time complexity, under the same assumption. The new algorithm is remarkably simple, consisting of just two fixed-point computations. We have implemented the algorithm and confirmed that it outperforms Kobayashi's previous algorithm in a certain case.

A type-directed abstraction refinement approach to higher-order model checking

“…Category 3. The final category consists of instances of a family of schemes due to Kobayashi [13]. This family of instances was designed to be deliberately difficult for bounded model checking style algorithms such as the hybrid algorithm of TRECS, whilst simultaneously being a good indicator of the scalability of Kobayashi's linear time algorithm as implemented in GTRECS.…”

“…The first fixed-parameter polytime (in the size of HORS) algorithm is GTRECS [13] which consists simply of two fixpoint constructions. The key innovation is a game-semantic reading of the intersection types qua a pair of expansion relations, modelling the legals moves of the two players of an arena game.…”

“…$15.00. http://dx.doi.org /10.1145/2535838.2535873 It is for these reasons, and despite the severe worst-case complexity of the problem 1 , that several ingenious algorithms [3,4,12,13,19] have recently been developed with the aim of solving the higher-order model checking problem for many "practical" instances. However, the state of this effort is summarised well by the authors of [3]:…”

An Intersection Type System for Deterministic Pushdown Automata

“…Kobayashi and Ong [7,9] have proposed a type system for recursion schemes that is equivalent to the modal µ-calculus model-checking of recursion schemes (the decidability of the model-checking problem has been proved by Ong [17]). These type systems have been applied to verification of higher-order programs [7,11,10], and practically effective typability checkers have been developed [6,8]. The present work extends type systems to deal with infinite state systems, namely deterministic pushdown automata.…”

A Saturation Method for Collapsible Pushdown Systems

“…A recent algorithm by Kobayashi speeds up his techniques using an over-approximating least fixed point computation to give an initial input to a greatest fixed point computation [22]. Like saturation this is a 'bottomup' approach and it would be interesting to see whether there are connections.…”