Minimizing finite automata is computationally hard

It is known that deterministic finite automata (DFAs) can be algorithmically minimized, i.e., a DFA M can be converted to an equivalent DFA M' which has a minimal number of states. The minimization can be done efficiently [6]. On the other hand, it is known that unambiguous finite automata (UFAs) and nondeterministic finite automata (NFAs) can be algorithmically minimized too, but their minimization problems turn out to be NP-complete and PSPACE-complete [8]. In this paper, the time complexity of the minimization problem for two restricted types of finite automata is investigated. These automata are nearly deterministic, since they only allow a small amount of non determinism to be used. On the one hand, NFAs with a fixed finite branching are studied, i.e., the number of nondeterministic moves within every accepting computation is bounded by a fixed finite number. On the other hand, finite automata are investigated which are essentially deterministic except that there is a fixed number of different initial states which can be chosen nondeterministically. The main result is that the minimization problems for these models are computationally hard, namely NP-complete. Hence, even the slightest extension of the deterministic model towards a nondeterministic one, e.g., allowing at most one nondeterministic move in every accepting computation or allowing two initial states instead of one, results in computationally intractable minimization problems

Models for extracting vertical crustal movements from leveling data

Various adjustment strategies are being used in North America to obtain vertical crustal movements from repeated leveling. The more successful models utilize polynomials or multiquadric analysis to describe elevation change with a velocity surface. Other features permit determination of nonlinear motions, motions associated with earthquakes or episodes, and vertical motions of blocks where boundaries are prespecified. The preferred models for estimating crustal motions permit the use of detached segments of releveling to govern the shape of a velocity surface and allow for input from nonleveling sources such as tide gages and paired lake gages. Some models for extracting vertical crustal movements from releveling data are also excellent for adjusting leveling networks, and permit mixing old and new data in areas exhibiting vertical motion. The new adjustment techniques are more general than older static models and will undoubtedly be used routinely in the future as the constitution of level networks becomes mainly relevelings

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Distinguishing sequences for partially specified FSMs

Distinguishing Sequences (DSs) are used inmany Finite State Machine (FSM) based test techniques. Although Partially Specified FSMs (PSFSMs) generalise FSMs, the computational complexity of constructing Adaptive and Preset DSs (ADSs/PDSs) for PSFSMs has not been addressed. This paper shows that it is possible to check the existence of an ADS in polynomial time but the corresponding problem for PDSs is PSPACE-complete. We also report on the results of experiments with benchmarks and over 8 * 106 PSFSMs. © 2014 Springer International Publishing

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

A Note on Fault Diagnosis Algorithms

In this paper we review algorithms for checking diagnosability of discrete-event systems and timed automata. We point out that the diagnosability problems in both cases reduce to the emptiness problem for (timed) B\"uchi automata. Moreover, it is known that, checking whether a discrete-event system is diagnosable, can also be reduced to checking bounded diagnosability. We establish a similar result for timed automata. We also provide a synthesis of the complexity results for the different fault diagnosis problems.Comment: Note: This paper is an extended version of the paper published in the proceedings of CDC'09, 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P.R. China, December 2009