Oscar H. Ibarra

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.

Moving Objects: Logical Relationships and Queries

In moving object databases, object locations in some multi-dimensional space depend on time. Previous work focuses mainly on moving object modeling (e.g., using ADTs, temporal logics) and ad hoc query optimization. In this paper we investigate logical properties of moving objects in connection with queries over such objects using tools from differential geometry. In an abstract model, object locations can be described as vectors of continuous functions of time. Using this conceptual model, we examine the logical relationships between moving objects, and between moving objects and (stationary) spatial objects in the database. We characterize these relationships in terms of position, velocity, and acceleration. We show that these fundamental relationships can be used to describe natural queries involving time instants and intervals. Based on this foundation, we develop a concrete data model for moving objects which is an extension of linear constraint databases. We also present a preliminary version of a logical query language for moving object databases.

Multi-tape and multi-head pushdown automata*

This paper considers multi-tape and multi-head extensions of various models of pushdown automata. One-way and two-way deterministic and nondeterministic multi-tape and multi-head pushdown automata are introduced and studied. The closure, characterization, and decision properties of the sets definable by these automata are iavestigated and the relationship between these sets and some well known families of languages is established.

Two-way pushdown automata

In this paper, a new type of automation, called a two-way pushdown automaton is defined and studied. The model is a generalization of a pushdown automaton in that two-way motion is allowed on the input tape which is assumed to have endmarkers. The model is investigated in both the nondeterministic and deterministic cases. A number of basic results are obtained which include relationships with other families, closure and nonclosure results, and decidability properties. Certain special cases are studied such as the cases when the input alphabet has one letter and the device has no endmarkers.

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 Number of Membranes Matters

We look at a restricted model of a communicating P system, called RCPS, whose environment does not contain any object initially. The system can expel objects into the environment but only expelled objects can be retrieved from the environment. Such a system is initially given an input \(a_1^{i_1} ... a_n^{i_n}\) (with each i j representing the multiplicity of distinguished object a i , 1 ≤ i ≤ n) and is used as an acceptor. We show that RCPS’s are equivalent to two-way multihead finite automata over bounded languages (i.e., subsets of \(a_1^* ... a_n^*\), for some distinct symbols a 1, ..., a n ). We then show that there is an infinite hierarchy of RCPS’s in terms of the number of membranes. In fact, for every r, there is an s> r and a unary language L accepted by an RCPS with s membranes that cannot be accepted by an RCPS with r membranes. This provides an answer to an open problem in [12] which asks whether there is a nonuniversal model of a membrane computing system which induces an infinite hierarchy on the number of membranes. We also consider variants/generalizations of RCPS’s, e.g., acceptors of languages; models that allow a “polynomial bounded” supply of objects in the environment initially; models with tentacles, etc. We show that they also form an infinite hierarchy with respect to the number of membranes (or tentacles). The proof techniques can be used to obtain similar results for other restricted models of P systems, like symport/antiport systems.

Adaptive Partitioning and Scheduling for Enhancing WWW Application Performance

This paper studies runtime partitioning, scheduling and load balancing techniques for improving performance of online WWW-based information systems such as digital libraries. The main performance bottlenecks of such a system are caused by the server computing capability and Internet bandwidth. Our observations and solutions are based on our experience with the Alexandria Digital Library (ADL) testbed at UCSB, which provides online browsing and processing of documents, digitized maps, and other geo-spatially mapped data via the WWW. A proper partitioning and scheduling of computation and communication in processing a user request on a multiprocessor server and transferring some computation to client-site machines can reduce network traffic and substantially improve system response time. We propose a partitioning and scheduling mechanism that adapts to resource changes and optimizes resource utilization and demonstrate the application of this mechanism for online information browsing. We also provide a performance analysis and experimental results to study the impact of resource availability and the effectiveness of our scheduling techniques.

New Decidability Results Concerning Two-way Counter Machines and Applications

We look at some decision questions concerning two-way counter machines and obtain the strongest decidable results to date concerning these machines. In particular, we show that the emptiness, containment, and equivalence problems are decidable for two-way counter machines whose counter is reversal-bounded (i.e., the counter alternates between increasing and decreasing modes at most a fixed number of times). We use this result to give a simpler proof of a recent result that the emptiness, containment, and equivalence problems for two-way reversal-bounded pushdown automata accepting bounded languages (i.e., subsets of w 1 * ... w k * for some nonnull words w1,...,wk) are decidable. Other applications concern decision questions about simple programs. Finally, we show that nondeterministic two-way reversal-bounded multicounter machines are effectively equivalent to finite automata on unary languages, and hence their emptiness, containment, and equivalence problems are decidable also.

Information Rate of Some Classes of Non-regular Languages: An Automata-Theoretic Approach

We show that the information rate of the language accepted by a reversal-bounded deterministic counter machine is computable. For the nondeterministic case, we provide computable upper bounds. For the class of languages accepted by multi-tape deterministic finite automata, the information rate is computable as well.

Decision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages

Let e be a class of automata (in a precise sense to be defined) and ec the class obtained by augmenting each automaton in e with finitely many reversal-bounded counters. We first show that if the languages defined by e are effectively semilinear, then so are the languages defined by ec, and, hence, their emptiness problem is decidable. This result is then used to show the decidability of various problems concerning morphisms and commutation of languages. We also prove a surprising undecidability result: given a fixed two element code K, it is undecidable whether a given context-free language L commutes with K, i.e., LK = KL.