Pushdown automata and constant height: Decidability and bounds: Extended abstract

It cannot be decided whether a pushdown automaton accepts using constant pushdown height, with respect to the input length, or not. Furthermore, in the case of acceptance in constant height, the height cannot be bounded by any recursive function in the size of the description of the machine. In contrast, in the restricted case of pushdown automata over a one-letter input alphabet, i.e., unary pushdown automata, the above property becomes decidable. Moreover, if the height is bounded by a constant in the input length, then it is at most exponential with respect to the size of the description of the pushdown automaton. This bound cannot be reduced. Finally, if a unary pushdown automaton uses nonconstant height to accept, then the height should grow at least as the logarithm of the input length. This bound is optimal

Conditional Lower Bounds for Space/Time Tradeoffs

In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on well-studied hardness assumptions such as 3SUM, APSP, SETH, etc. This line of research helps to obtain a better understanding of the complexity inside P. A related question asks to prove conditional space lower bounds on data structures that are constructed to solve certain algorithmic tasks after an initial preprocessing stage. This question received little attention in previous research even though it has potential strong impact. In this paper we address this question and show that surprisingly many of the well-studied hard problems that are known to have conditional polynomial time lower bounds are also hard when concerning space. This hardness is shown as a tradeoff between the space consumed by the data structure and the time needed to answer queries. The tradeoff may be either smooth or admit one or more singularity points. We reveal interesting connections between different space hardness conjectures and present matching upper bounds. We also apply these hardness conjectures to both static and dynamic problems and prove their conditional space hardness. We believe that this novel framework of polynomial space conjectures can play an important role in expressing polynomial space lower bounds of many important algorithmic problems. Moreover, it seems that it can also help in achieving a better understanding of the hardness of their corresponding problems in terms of time

Constraints Propagation on GPU: A Case Study for AllDifferent

The AllDifferent constraint is a fundamental tool in Constraint Programming. It naturally arises in many problems, from puzzles to scheduling and routing applications. Such popularity has prompted an extensive literature on filtering and propagation for this constraint. Motivated by the benefits that GPUs offer to other branches of AI, this paper investigates the use of GPUs to accelerate filtering and propagation. In particular, we present an efficient parallelization of the AllDifferent constraint on GPU; we analyze different design and implementation choices and evaluates the performance of the resulting system on medium to large instances of the Travelling Salesman Problem with encouraging results

Nearly Optimal Separation Between Partially and Fully Retroactive Data Structures

Since the introduction of retroactive data structures at SODA 2004, a major unsolved problem has been to bound the gap between the best partially retroactive data structure (where changes can be made to the past, but only the present can be queried) and the best fully retroactive data structure (where the past can also be queried) for any problem. It was proved in 2004 that any partially retroactive data structure with operation time T_{op}(n,m) can be transformed into a fully retroactive data structure with operation time O(sqrt{m} * T_{op}(n,m)), where n is the size of the data structure and m is the number of operations in the timeline [Demaine et al., 2004]. But it has been open for 14 years whether such a gap is necessary. In this paper, we prove nearly matching upper and lower bounds on this gap for all n and m. We improve the upper bound for n << sqrt m by showing a new transformation with multiplicative overhead n log m. We then prove a lower bound of min {n log m, sqrt m}^{1-o(1)} assuming any of the following conjectures: - Conjecture I: Circuit SAT requires 2^{n - o(n)} time on n-input circuits of size 2^{o(n)}. This conjecture is far weaker than the well-believed SETH conjecture from complexity theory, which asserts that CNF SAT with n variables and O(n) clauses already requires 2^{n-o(n)} time. - Conjecture II: Online (min,+) product between an integer n x n matrix and n vectors requires n^{3 - o(1)} time. This conjecture is weaker than the APSP conjectures widely used in fine-grained complexity. - Conjecture III (3-SUM Conjecture): Given three sets A,B,C of integers, each of size n, deciding whether there exist a in A, b in B, c in C such that a + b + c = 0 requires n^{2 - o(1)} time. This 1995 conjecture [Anka Gajentaan and Mark H. Overmars, 1995] was the first conjecture in fine-grained complexity. Our lower bound construction illustrates an interesting power of fully retroactive queries: they can be used to quickly solve batched pair evaluation. We believe this technique can prove useful for other data structure lower bounds, especially dynamic ones

Revisiting Membership Problems in Subclasses of Rational Relations

We revisit the membership problem for subclasses of rational relations over finite and infinite words: Given a relation R in a class C_2, does R belong to a smaller class C_1? The subclasses of rational relations that we consider are formed by the deterministic rational relations, synchronous (also called automatic or regular) relations, and recognizable relations. For almost all versions of the membership problem, determining the precise complexity or even decidability has remained an open problem for almost two decades. In this paper, we provide improved complexity and new decidability results. (i) Testing whether a synchronous relation over infinite words is recognizable is NL-complete (PSPACE-complete) if the relation is given by a deterministic (nondeterministic) omega-automaton. This fully settles the complexity of this recognizability problem, matching the complexity of the same problem over finite words. (ii) Testing whether a deterministic rational binary relation is recognizable is decidable in polynomial time, which improves a previously known double exponential time upper bound. For relations of higher arity, we present a randomized exponential time algorithm. (iii) We provide the first algorithm to decide whether a deterministic rational relation is synchronous. For binary relations the algorithm even runs in polynomial time

Homomorphic Encryption for Finite Automata

We describe a somewhat homomorphic GSW-like encryption scheme, natively encrypting matrices rather than just single elements. This scheme offers much better performance than existing homomorphic encryption schemes for evaluating encrypted (nondeterministic) finite automata (NFAs). Differently from GSW, we do not know how to reduce the security of this scheme to LWE, instead we reduce it to a stronger assumption, that can be thought of as an inhomogeneous variant of the NTRU assumption. This assumption (that we term iNTRU) may be useful and interesting in its own right, and we examine a few of its properties. We also examine methods to encode regular expressions as NFAs, and in particular explore a new optimization problem, motivated by our application to encrypted NFA evaluation. In this problem, we seek to minimize the number of states in an NFA for a given expression, subject to the constraint on the ambiguity of the NFA

Annual Report, 2013-2014

Beginning in 2004/2005- issued in online format onl

Remote Sensing of Earth Resources: A literature survey with indexes (1970 - 1973 supplement). Section 1: Abstracts

Abstracts of reports, articles, and other documents introduced into the NASA scientific and technical information system between March 1970 and December 1973 are presented in the following areas: agriculture and forestry, environmental changes and cultural resources, geodesy and cartography, geology and mineral resources, oceanography and marine resources, hydrology and water management, data processing and distribution systems, instrumentation and sensors, and economic analysis

Faculty Publications and Creative Works 2004

Faculty Publications & Creative Works is an annual compendium of scholarly and creative activities of University of New Mexico faculty during the noted calendar year. Published by the Office of the Vice President for Research and Economic Development, it serves to illustrate the robust and active intellectual pursuits conducted by the faculty in support of teaching and research at UNM