Higher-Order Model Checking Step by Step

by   Paweł Parys, et al.

We show a new simple algorithm that solves the model-checking problem for recursion schemes: check whether the tree generated by a given higher-order recursion scheme is accepted by a given alternating parity automaton. The algorithm amounts to a procedure that transforms a recursion scheme of order n to a recursion scheme of order n-1, preserving acceptance, and increasing the size only exponentially. After repeating the procedure n times, we obtain a recursion scheme of order 0, for which the problem boils down to solving a finite parity game. Since the size grows exponentially at each step, the overall complexity is n-EXPTIME, which is known to be optimal. More precisely, the transformation is linear in the size of the recursion scheme, assuming that the arity of employed nonterminals and the size of the automaton are bounded by a constant; this results in an FPT algorithm for the model-checking problem. Our transformation is a generalization of a previous transformation of the author (2020), working for reachability automata in place of parity automata. The step-by-step approach can be opposed to previous algorithms solving the considered problem "in one step", being compulsorily more complicated.


page 1

page 2

page 3

page 4


Higher-Order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

This paper studies the logical properties of a very general class of inf...

A Survey on Satisfiability Checking for the μ-Calculus through Tree Automata

Algorithms for model checking and satisfiability of the modal μ-calculus...

Simple Fixpoint Iteration To Solve Parity Games

A naive way to solve the model-checking problem of the mu-calculus uses ...

Higher-Order Bounded Model Checking

We present a Bounded Model Checking technique for higher-order programs....

Recursion Schemes, the MSO Logic, and the U quantifier

We study the model-checking problem for recursion schemes: does the tree...

Experimental Study on CTL model checking using Machine Learning

The existing core methods, which are employed by the popular CTL model c...

Computing Nested Fixpoints in Quasipolynomial Time

It is well known that the winning region of a parity game with n nodes a...

Please sign up or login with your details

Forgot password? Click here to reset