Zhe Dang

Binary Reachability Analysis of Discrete Pushdown Timed Automata

We introduce discrete pushdown timed automata that are timed automata with integer-valued clocks augmented with a pushdown stack. A configuration of a discrete pushdown timed automaton includes a control state, finitely many clock values and a stack word. Using a pure automata-theoretic approach, we show that the binary reachability (i.e., the set of all pairs of configurations (α,β), encoded as strings, such that α can reach β through 0 or more transitions) can be accepted by a nondeterministic pushdown machine augmented with reversal-bounded counters (NPCM). Since discrete timed automata with integer-valued clocks can be treated as discrete pushdown timed automata without the pushdown stack, we can show that the binary reachability of a discrete timed automaton can be accepted by a nondeterministic reversal-bounded multicounter machine. Thus, the binary reachability is Presburger. By using the known fact that the emptiness problem is decidable for reversal-bounded NPCMs, the results can be used to verify a number of properties that can not be expressed by timed temporal logics for discrete timed automata and CTL* for pushdown systems.

Binary Reachability Analysis of Pushdown Timed Automata with Dense Clocks

We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability (i.e., the set of all pairs of configurations such that one can reach the other) of a PTA. Since a timed automaton can be treated as a PTA without the pushdown stack, we can show that the binary reachability of a timed automaton is definable in the additive theory of reals and integers. The results can be used to verify a class of properties containing linear relations over both dense variables and unbounded discrete variables. The properties previously could not be verified using the classic region technique nor expressed by timed temporal logics for timed automata and CTL* for pushdown systems.

ON STATELESS AUTOMATA AND P SYSTEMS

We introduce the notion of stateless multihead two-way (respectively, one-way) NFAs and stateless multicounter systems and relate them to P systems and vector addition systems. In particular, we investigate the decidability of the emptiness and reachability problems for these stateless automata and show that the results are applicable to similar questions concerning certain variants of P systems, namely, token systems and sequential tissue-like P systems.

Using the ASTRAL model checker to analyze mobile IP

ASTRAL is a high level formal specification language for real time systems. It is provided with structuring mechanisms that allow one to build modularized specifications of complex real time systems with layering. The ASTRAL model checker checks the satisfiability of critical requirements of a specification by enumerating possible runs of transitions within a given time bound. The paper discusses the mechanism of the model checker and how it can be used to analyze encryption protocols. Several classic benchmarks have been investigated, including the Needham-Schroeder public-key authentication protocol (R.M. Needham and M.D. Schroeder, 1978) and the TMN protocol, and a number of attacks were uncovered. The paper focuses on using ASTRAL to specify Mobile IP (C. Perkins, 1996) and testing the specification using the model checker.

A solvable class of quadratic Diophantine equations with applications to verification of infinite-state systems

A k-system consists of k quadratic Diophantine equations over nonnegative integer variables s1, ..., sm, t1, ..., tn of the form: Σ 1≤j≤l B1j(t1, ..., tn)A1j(s1, ..., sm) = C1(s1, ..., sm) Σ 1≤j≤l Bkj(t1, ..., tn)Akj(s1, ..., sm) = Ck(s1, ..., sm) where l, n, m are positive integers, the Bs are nonnegative linear polynomials over t1, ..., tn (i.e., they are of the form b0+b1t1+...+bntn, where each bi is a nonnegative integer), and the As and Cs are nonnegative linear polynomials over s1, ..., sm. We show that it is decidable to determine, given any 2-system, whether it has a solution in s1, ..., sm, t1, ..., tn, and give applications of this result to some interesting problems in verification of infinite-state systems. The general problem is undecidable; in fact, there is a fixed k > 2 for which the k-system problem is undecidable. However, certain special cases are decidable and these, too, have applications to verification.

Liveness Verification of Reversal-Bounded Multicounter Machines with a Free Counter

We investigate the Presburger liveness problems for nondeterministic reversal-bounded multicounter machines with a free counter (NCMFs). We show the following: - The ∃-Presburger-i.o. problem and the ∃-Presburger-eventual problem are both decidable. So are their duals, the ∀-Presburger-almost-always problem and the ∀-Presburger-always problem. - The ∀-Presburger-i.o. problem and the ∀-Presburger-eventual problem are both undecidable. So are their duals, the ∃-Presburger-almost-always problem and the ∃-Presburger-always problem. These results can be used to formulate a weak form of Presburger linear temporal logic and developits model-checking theories for NCMFs. They can also be combined with [12] to study the same set of liveness problems on an extended form of discrete timed automata containing, besides clocks, a number of reversal-bounded counters and a free counter.

The design and analysis of real-time systems using the ASTRAL software development environment

ASTRAL is a formal specification language for real-time systems. It is intended to support formal software development and, therefore, has been formally defined. The structuring mechanisms in ASTRAL allow one to build modularized specifications of complex systems with layering. A real-time system is modeled by a collection of state machine specifications and a single global specification. This paper discusses the ASTRAL Software Development Environment (SDE), which is an integrated set of design and analysis tools based on the ASTRAL formal framework. The tools that make up the support environment are a syntax-directed editor, a specification processor, a verification condition generator, a browser kit, a model checker, and a mechanical theorem prover.

Composability of infinite-state activity automata

Let

The power of maximal parallelism in p systems

{\mathcal M}

Presburger liveness verification of discrete timed automata

be a class of (possibly nondeterministic) language acceptors with a one-way input tape A system (A; A1, ..., Ar) of automata in