Yih-Kuen Tsay

Algorithmic analysis of programs with well quasi-ordered domains

Over the past few years increasing research effort has been directed towards the automatic verification of infinite-state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems) which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a preorder which is a well quasi-ordering, such that the transition relation is “monotonic” (a simulation) with respect to the preorder. We show that the following properties are decidable for well-structured systems: ?Reachability: whether a certain set of control states is reachable. Other safety properties can be reduced to the reachability problem. ?Eventuality: whether all executions eventually reach a given set of control states (represented as AFp in CTL). ?Simulation: whether there exists a simulation between a finite automaton and a well-structured system. The simulation problem will be shown to be decidable in both directions. We also describe how these general principles subsume several decidability results from the literature about timed automata, relational automata, Petri nets, and lossy channel systems.

Automatic numeric abstractions for heap-manipulating programs

We present a logic for relating heap-manipulating programs to numeric abstractions. These numeric abstractions are expressed as simple imperative programs over integer variables and have the property that termination and safety of the numeric program ensures termination and safety of the original, heap-manipulating program. We have implemented an automated version of this abstraction process and present experimental results for programs involving a variety of data structures.

Assumption/guarantee specifications in linear-time temporal logic

An assumption/guarantee specification of a system consists of an assumption part, which specifies the assumptions on the behavior of the environment, and a guarantee part, which specifies the prope ...

Learning Minimal Separating DFA's for Compositional Verification

Algorithms for learning a minimal separating DFA of two disjoint regular languages have been proposed and adapted for different applications. One of the most important applications is learning minimal contextual assumptions in automated compositional verification. We propose in this paper an efficient learning algorithm, called , that learns and generates a minimal separating DFA. Our algorithm has a quadratic query complexity in the product of sizes of the minimal DFAs for the two input languages. In contrast, the most recent algorithm of Gupta et al. has an exponential query complexity in the sizes of the two DFAs. Moreover, experimental results show that our learning algorithm significantly outperforms all existing algorithms on randomly-generated example problems. We describe how our algorithm can be adapted for automated compositional verification. The adapted version is evaluated on the LTSA benchmarks and compared with other automated compositional verification approaches. The result shows that our algorithm surpasses others in 30 of 49 benchmark problems.

THOR: A Tool for Reasoning about Shape and Arithmetic

We describe T hor ( T ool for H eap- O riented R easoning), a tool based on separation logic that is capable of reasoning automatically about heap-manipulating programs. There are several such systems in development now. However, T hor is unique in that it provides not only shape analysis, but also arithmetic reasoning via a novel combination procedure. Also, considerable effort has been put into making the output clear and easy to understand. T hor uses Javascript and HTML to produce an interactive representation of the analysis results.

Extending automated compositional verification to the full class of omega-regular languages

Recent studies have suggested the applicability of learning to automated compositional verification. However, current learning algorithms fall short when it comes to learning liveness properties. We extend the automaton synthesis paradigm for the infinitary languages by presenting an algorithm to learn an arbitrary regular set of infinite sequences (an ω-regular language) over an alphabet Σ. Our main result is an algorithm to learn a nondeterministic Buchi automaton that recognizes an unknown ω-regular language. This is done by learning a unique projection of it on Σ* using the framework suggested by Angluin for learning regular subsets of Σ*.

GOAL: a graphical tool for manipulating Büchi automata and temporal formulae

In this paper, we present a tool named GOAL (an acronym derived from “Graphical Tool for Omega-Automata and Logics”) whose main functions include (1) drawing and testing Buchi automata, (2) checking the language equivalence between two Buchi automata, (3) translating quantified propositional linear temporal logic (QPTL) formulae into equivalent Buchi automata, and (4) exporting Buchi automata as Promela code. The GOAL tool, available at http://goal.im.ntu.edu.tw, can be used for educational purposes, helping the user get a better understanding of how Buchi automata work and how they are related to linear temporal logics. It may also be used, as we shall explain below, to construct correct and smaller specification automata, supplementing model checkers that adopt the automata-theoretic approach, such as SPIN [5].

Automated assume-guarantee reasoning through implicit learning

We propose a purely implicit solution to the contextual assumption generation problem in assume-guarantee reasoning Instead of improving the L* algorithm — a learning algorithm for finite automata, our algorithm computes implicit representations of contextual assumptions by the CDNF algorithm — a learning algorithm for Boolean functions We report three parametrized test cases where our solution outperforms the monolithic interpolation-based Model Checking algorithm.

GOAL extended: towards a research tool for omega automata and temporal logic

This paper reports extensions to the GOAL tool that enable it to become a research tool for omega automata and temporal logic. The extensions include an expanded collection of translation, simplification, and complementation algorithms, a command-line mode which makes GOAL functions accessible by programs, and utility functions for such common tasks as file format conversion, random formulae generation, and statistics collection.

State of büchi complementation

Buchi complementation has been studied for five decades since the formalism was introduced in 1960. Known complementation constructions can be classified into Ramsey-based, determinization-based, rank-based, and slice-based approaches. For the performance of these approaches, there have been several complexity analyses but very few experimental results. What especially lacks is a comparative experiment on all the four approaches to see how they perform in practice. In this paper, we review the state of Buchi complementation, propose several optimization heuristics, and perform comparative experimentation on the four approaches. The experimental results show that the determinizationbased Safra-Piterman construction outperforms the other three and our heuristics substantially improve the Safra-Piterman construction and the slice-based construction.