Ranko Lazić

On the freeze quantifier in constraint LTL: decidability and complexity

Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some real-time logics, but this variable-binding mechanism is quite general and ubiquitous in many logical languages (first-order temporal logics, hybrid logics, logics for sequence diagrams, navigation logics, etc.). We show that Constraint LTL over the simple domain augmented with the freeze operator is undecidable which is a surprising result regarding the poor language for constraints (only equality tests). Many versions of freeze-free constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes /spl Sigma//sub 1//sup 1/ -completeness. On the positive side, we provide complexity results when the domain is finite (EXPSPACE-completeness) or when the formulae are flat in a sense introduced in the paper.

A Unifying Approach to Data-Independence

A concurrent system is data-independent with respect to a data type when the only operation it can perform on values of that type is equality testing. The system can also assign, input, nondeterministically choose, and output such values. Based on this intuitive definition, syntactic restrictions which ensure data-independence have been formulated for a variety of different formalisms. However, it is difficult to see how these are related. We present the first semantic definition of data-independence which allows equality testing, and its extension which allows constant symbols and predicate symbols. Both are special cases of a definition of when a family of labelled transition systems is parametric. This provides a unified approach to data-independence and its extensions. The paper also contains two theorems which, given a system and a specification which are data-independent, enable the verification for all instantiations of the data types (and of the constant symbols and the predicate symbols, in the case of the extension) to be reduced to the verification for a finite number of finite instantiations. We illustrate the applicability of the approach to particular formalisms by a programming language similar to UNITY.

The covering and boundedness problems for branching vector addition systems

The covering and boundedness problems for branching vector addition systems are shown complete for doubly-exponential time.

Nets with tokens which carry data

We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which whole-place operations such as resets and transfers are possible. Data nets subsume several known classes of infinite-state systems, including multiset rewriting systems and polymorphic systems with arrays. We show that coverability and termination are decidable for arbitrary data nets, and that boundedness is decidable for data nets in which whole-place operations are restricted to transfers. By providing an encoding of lossy channel systems into data nets without whole-place operations, we establish that coverability, termination and boundedness for the latter class have non-primitive recursive complexity. The main result of the paper is that, even for unordered data domains (i.e., with only the equality predicate), each of the three verification problems for data nets without whole-place operations has non-elementary complexity.

Model checking freeze LTL over one-counter automata

We study complexity issues related to the model-checking problem for LTL with registers (a.k.a. freeze LTL) over one-counter automata. We consider several classes of one-counter automata (mainly deterministic vs. nondeterministic) and several syntactic fragments (restriction on the number of registers and on the use of propositional variables for control locations). The logic has the ability to store a counter value and to test it later against the current counter value. By introducing a non-trivial abstraction on counter values, we show that model checking LTL with registers over deterministic one-counter automata is PSPACE-complete with infinite accepting runs. By constrast, we prove that model checking LTL with registers over nondeterministic one-counter automata is Σ11 -complete [resp. Σ10-complete] in the infinitary [resp. finitary] case even if only one register is used and with no propositional variable. This makes a difference with the facts that several verification problems for one-counter automata are known to be decidable with relatively low complexity, and that finitary satisfiability for LTL with a unique register is decidable. Our results pave the way for model-checking LTL with registers over other classes of operational models, such as reversal-bounded counter machines and deterministic pushdown systems.

Data-abstraction refinement: a game semantic approach

This paper presents a semantic framework for data abstraction and refinement for verifying safety properties of open programs. The presentation is focused on an Algol-like programming language that incorporates data abstraction in its syntax. The fully abstract game semantics of the language is used for model-checking safety properties, and an interaction-sequence-based semantics is used for interpreting potentially spurious counterexamples and computing refined abstractions for the next iteration.

Safely freezing LTL

We consider the safety fragment of linear temporal logic with the freeze quantifier. The freeze quantifier is used to store a value from an infinite domain in a register for later comparison with other such values. We show that, for one register, satisfiability, refinement and model checking problems are decidable. The main result in the paper is that satisfiability is ExpSPACE-complete. The proof of EXPSPACE-membership involves a translation to a new class of faulty counter automata. We also show that refinement and model checking are not primitive recursive, and that dropping the safety restriction, adding past-time temporal operators, or adding one more register, each cause undecidability of all three decision problems.

On model checking data-independent systems with arrays without reset

A system is data-independent with respect to a data type

Alternating automata on data trees and XPath satisfiability

X

Average-Price and Reachability-Price Games on Hybrid Automata with Strong Resets

iff the operations it can perform on values of type