Anthony Widjaja Lin

Expressive Languages for Path Queries over Graph-Structured Data

For many problems arising in the setting of graph querying (such as finding semantic associations in RDF graphs, exact and approximate pattern matching, sequence alignment, etc.), the power of standard languages such as the widely studied conjunctive regular path queries (CRPQs) is insufficient in at least two ways. First, they cannot output paths and second, more crucially, they cannot express relationships among paths. We thus propose a class of extended CRPQs, called ECRPQs, which add regular relations on tuples of paths, and allow path variables in the heads of queries. We provide several examples of their usefulness in querying graph structured data, and study their properties. We analyze query evaluation and representation of tuples of paths in the output by means of automata. We present a detailed analysis of data and combined complexity of queries, and consider restrictions that lower the complexity of ECRPQs to that of relational conjunctive queries. We study the containment problem, and look at further extensions with first-order features, and with nonregular relations that add arithmetic constraints on the lengths of paths and numbers of occurrences of labels.

Model checking recursive programs with numeric data types

Pushdown systems (PDS) naturally model sequential recursive programs. Numeric data types also often arise in real-world programs. We study the extension of PDS with unbounded counters, which naturally model numeric data types. Although this extension is Turingpowerful, reachability is known to be decidable when the number of reversals between incrementing and decrementing modes is bounded. In this paper, we (1) pinpoint the decidability/complexity of reachability and linear/branching time model checking over PDS with reversal-bounded counters (PCo), and (2) experimentally demonstrate the effectiveness of our approach in analysing software. We show reachability over PCo is NP-complete, while LTL is coNEXP-complete (coNP-complete for fixed formulas). In contrast, we prove that EF-logic over PCo is undecidable. Our NP upper bounds are by a direct poly-time reduction to satisfaction over existential Presburger formulas, allowing us to tap into highly optimized solvers like Z3. Although reversal-bounded analysis is incomplete for PDS with unbounded counters in general, our experiments suggest that some intricate bugs (e.g. from Linux device drivers) can be discovered with a small number of reversals. We also pinpoint the decidability/ complexity of various extensions of PCo, e.g., with discrete clocks.

Synchronisation- and reversal-bounded analysis of multithreaded programs with counters

We study a class of concurrent pushdown systems communicating by both global synchronisations and reversal-bounded counters, providing a natural model for multithreaded programs with procedure calls and numeric data types. We show that the synchronisation-bounded reachability problem can be efficiently reduced to the satisfaction of an existential Presburger formula. Hence, the problem is NP-complete and can be tackled with efficient SMT solvers such as Z3. In addition, we present optimisations to make our reduction practical, e.g., heuristics for removing or merging transitions in our models. We provide optimised algorithms and a prototypical implementation of our results and perform preliminary experiments on examples derived from real-world problems.

The Complexity of Verifying Ground Tree Rewrite Systems

Ground tree rewrite systems (GTRS) are an extension of pushdown systems with the ability to spawn new sub threads that are hierarchically structured. In this paper, we study the following problems over GTRS:(1) model checking EF-logic, (2)weak bi similarity checking against finite systems, and (3) strong similarity against finite systems. Although they are all known to be decidable, we show that problems (1) and (2) have nonelementbisimilarityy, whereasproblem (3) is shown to be in

Accelerating tree-automatic relations

\coNEXP

Refining the Process Rewrite Systems Hierarchy via Ground Tree Rewrite Systems

by finding a syntactic fragment of EFwhose model checking complexity is complete for

String constraints with concatenation and transducers solved efficiently

\P^\NEXP

Concurrency Makes Simple Theories Hard

.The same problems are studied over a more general but decidable extension of GTRS called regular GTRS (RGTRS), where regular rewriting is allowed. Over RGTRS we show that all three problems have non elementary complexity. We also apply our techniques to problems over PA-processes, a well-known class of infinite systems in Mayrs PRS (Process Rewrite Systems) hierarchy. For example, strong bi similarity checking of PA-processes against finite systems is shown to be in

Refining the process rewrite systems hierarchy via ground tree rewrite systems

\coNEXP

Liveness of Randomised Parameterised Systems under Arbitrary Schedulers

, yielding a first elementary upper bound for this problem.