Dynamic programs, or fixpoint iteration schemes, are useful for solving many problems on state spaces, including model checking on Kripke structures (“verification”), computing shortest paths on weighted graphs (“optimization”), computing the value of games played on game graphs (“control”). For Kripke structures, a rich fixpoint theory is available in the form of the μ-calculus. Yet few connec...

In this article, we give an overview of our project on higher-order program verification based HFL (higher-order fixpoint logic) model checking. After a brief introduction to HFL, explain how it can be applied verification, and summarize the current status project.

The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. The goal of this paper is to extend Gentzen’s sequent calculus to obtain a deductive inference method for FO(ID). The main difficulty in building such a proof system is the representation and inference of unfounded sets. It turns out that we can represent unfounde...

Experiment on a Modular Program Aanlysis That Saves Memory Jaehwang Kim School of Computer Science and Engineering College of Engineering Seoul National University We present a modular fixpoint computation that consumes smaller memory than a global fixpoint iterations yet with no loss of accuracy. Our motivation comes from designing a scalable global program analysis. Program analysis is to com...

It is desirable to answer queries posed to deductive databases by computing fix-points because such computations are directly amenable to set-oriented fact processing. However, the classical fixpoint procedures based on bottom-up reasoning-the naive and semi-naive methods-are rather primitive and often inefficient. In this article, we rely on bottom-up meta-interpretation for formalizing a new ...

In this paper a fixpoint iteration for reachability analysis of infinite transition systems is presented that can be applied to the verification of circuits at register-transfer level. It is assumed that the system is modeled by using interpreted and uninterpreted functions. To represent infinite sets of states a data structure called symbolic state is introduced. A procedure for deciding the s...

A wide range of additional forward chaining applications could be realized with deductive databases, if their rule formalism, their immediate consequence operator, and their fixpoint iteration process would be more flexible. Deductive databases normally represent knowledge using stratified Datalog programs with default negation. But many practical applications of forward chaining require an ext...

We propose a nonparametric cluster algorithm based on local medians. Each observation is substituted by its local median and this new observation moves toward the peaks and away from the valleys of the distribution. The process is repeated until each observation converges to a fixpoint. We obtain a partition of the sample based on the convergence points. Our algorithm determines the number of c...

We present MLSolver, a tool for solving the satisfiability and validity problems for modal fixpoint logics. The underlying technique is based on characterisations of satisfiability through infinite (cyclic) tableaux in which branches have an inner thread structure mirroring the regeneration of least and greatest fixpoint constructs in the infinite. Well-foundedness for unfoldings of least fixpo...

We propose a modal logic programming language called MProlog, which is as expressive as the general modal Horn fragment. We give a fixpoint semantics and an SLD-resolution calculus for MProlog in all of the basic serial modal logics KD , T , KDB , B , KD4, S4, KD5, KD45, and S5. For an MProlog program P and for L being one of the mentioned logics, we define an operator TL,P , which has the leas...