The emptiness problem for tree automata with at least one global disequality constraint is NP-hard

2017 ◽  
Vol 118 ◽  
pp. 6-9 ◽  
Author(s):  
P.-C. Héam ◽  
V. Hugot ◽  
O. Kouchnarenko
Keyword(s):  
Np Hard ◽  
Tree Automata ◽  
Emptiness Problem

SYSTOLIC TREE WITH BASE AUTOMATA

1991 ◽  
Vol 02 (03) ◽  
pp. 221-236 ◽  
Author(s):  
A. MONTI ◽  
D. PARENTE
Keyword(s):  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Emptiness Problem ◽  
Necessary And Sufficient ◽  
Natural Way

Different systolic tree automata (STA) with base (T(b)−STA) are compared. This is a subclass of STA with interesting properties of modularity. We give a necessary and sufficient condition for the inclusion between classes of languages accepted by T(b)− STA, (L(T(b)−STA)), as b varies. We focus on T(b)−STA obtained by varying the base b in a natural way. We prove that for every base b within this framework there exists an a such that L(T(a)−STA) is not contained in L(T(b)−STA). We characterize the family of languages accepted by T(b)−STA when the input conditions are relaxed. Moreover we show that the emptiness problem is decidable for T(b)−STA.

Projection for Büchi Tree Automata with Constraints between Siblings

2020 ◽  
Vol 31 (06) ◽  
pp. 749-775
Author(s):  
Patrick Landwehr ◽  
Christof Löding
Keyword(s):  
Decision Procedure ◽  
Order Logic ◽  
Tree Automata ◽  
Boolean Operations ◽  
Regular Tree ◽  
Infinite Trees ◽  
Acceptance Condition ◽  
Emptiness Problem ◽  
Second Order Logic ◽  
Monadic Second Order Logic

We consider an extension of tree automata on infinite trees that can use equality and disequality constraints between direct subtrees of a node. Recently, it has been shown that the emptiness problem for these kind of automata with a parity acceptance condition is decidable and that the corresponding class of languages is closed under Boolean operations. In this paper, we show that the class of languages recognizable by such tree automata with a Büchi acceptance condition is closed under projection. This construction yields a new algorithm for the emptiness problem, implies that a regular tree is accepted if the language is non-empty (for the Büchi condition), and can be used to obtain a decision procedure for an extension of monadic second-order logic with predicates for subtree comparisons.

RELATING TREE SERIES TRANSDUCERS AND WEIGHTED TREE AUTOMATA

2005 ◽  
Vol 16 (04) ◽  
pp. 723-741 ◽  
Author(s):  
ANDREAS MALETTI
Keyword(s):  
Tree Automata ◽  
Formal Representation ◽  
Weighted Tree ◽  
Bottom Up ◽  
Operation Symbol ◽  
Tree Series ◽  
Pumping Lemma ◽  
Emptiness Problem ◽  
Weighted Tree Automata ◽  
The Given

Bottom-up tree series transducers (tst) over the semiring [Formula: see text] are implemented with the help of bottom-up weighted tree automata (wta) over an extension of [Formula: see text]. Therefore bottom-up [Formula: see text]-weighted tree automata ([Formula: see text]-wta) with [Formula: see text] a distributive Ω-algebra are introduced. A [Formula: see text]-wta is essentially a wta but uses as transition weight an operation symbol of the Ω-algebra [Formula: see text] instead of a semiring element. The given tst is implemented with the help of a [Formula: see text]-wta, essentially showing that [Formula: see text]-wta are a joint generalization of tst (using IO-substitution) and wta. Then a semiring and a wta are constructed such that the wta computes a formal representation of the semantics of the [Formula: see text]-wta. The applicability of the obtained presentation result is demonstrated by deriving a pumping lemma for deterministic finite [Formula: see text]-wta from a known pumping lemma for deterministic finite wta. Finally, it is observed that the known decidability results for emptiness cannot be applied to obtain decidability of emptiness for finite [Formula: see text]-wta. Thus with help of a weaker version of the derived pumping lemma, decidability of the emptiness problem for finite [Formula: see text]-wta is shown under mild conditions on [Formula: see text].

scholarly journals The Emptiness Problem for Tree Automata with Global Constraints

2010 ◽  
Author(s):  
Luis Barguno ◽  
Carles Creus ◽  
Guillem Godoy ◽  
Florent Jacquemard ◽  
Camille Vacher
Keyword(s):  
Global Constraints ◽  
Tree Automata ◽  
Emptiness Problem

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

scholarly journals Optimizing Transmit Sequence and Instrumental Variables Receiver for Dual-Function Complexity System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yu Yao ◽  
Junhui Zhao ◽  
Lenan Wu
Keyword(s):  
Approximate Solution ◽  
Instrumental Variables ◽  
Performance Index ◽  
Dual Function ◽  
Np Hard ◽  
Match Filter ◽  
Filter Output ◽  
Phase Code ◽  
Discrete Phase ◽  
Simulation Results

This correspondence deals with the joint cognitive design of transmit coded sequences and instrumental variables (IV) receive filter to enhance the performance of a dual-function radar-communication (DFRC) system in the presence of clutter disturbance. The IV receiver can reject clutter more efficiently than the match filter. The signal-to-clutter-and-noise ratio (SCNR) of the IV filter output is viewed as the performance index of the complexity system. We focus on phase only sequences, sharing both a continuous and a discrete phase code and develop optimization algorithms to achieve reasonable pairs of transmit coded sequences and IV receiver that fine approximate the behavior of the optimum SCNR. All iterations involve the solution of NP-hard quadratic fractional problems. The relaxation plus randomization technique is used to find an approximate solution. The complexity, corresponding to the operation of the proposed algorithms, depends on the number of acceptable iterations along with on and the complexity involved in all iterations. Simulation results are offered to evaluate the performance generated by the proposed scheme.

Multiple Regularity and Binary ETOL-Systems1

1981 ◽  
Vol 4 (1) ◽  
pp. 19-34
Author(s):  
Ryszard Danecki
Keyword(s):  
Equivalence Problem ◽  
Tree Automata ◽  
Closure Properties ◽  
Multiple Tree

Closure properties of binary ETOL-languages are investigated by means of multiple tree automata. Decidability of the equivalence problem of deterministic binary ETOL-systems is proved.

On the Complexity of Deadlock Recovery

1986 ◽  
Vol 9 (3) ◽  
pp. 323-342
Author(s):  
Joseph Y.-T. Leung ◽  
Burkhard Monien
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Arbitrary Number ◽  
The Other ◽  
Np Hard ◽  
Total Cost ◽  
Other Hand ◽  
Input Parameters ◽  
Resource Type

We consider the computational complexity of finding an optimal deadlock recovery. It is known that for an arbitrary number of resource types the problem is NP-hard even when the total cost of deadlocked jobs and the total number of resource units are “small” relative to the number of deadlocked jobs. It is also known that for one resource type the problem is NP-hard when the total cost of deadlocked jobs and the total number of resource units are “large” relative to the number of deadlocked jobs. In this paper we show that for one resource type the problem is solvable in polynomial time when the total cost of deadlocked jobs or the total number of resource units is “small” relative to the number of deadlocked jobs. For fixed m ⩾ 2 resource types, we show that the problem is solvable in polynomial time when the total number of resource units is “small” relative to the number of deadlocked jobs. On the other hand, when the total number of resource units is “large”, the problem becomes NP-hard even when the total cost of deadlocked jobs is “small” relative to the number of deadlocked jobs. The results in the paper, together with previous known ones, give a complete delineation of the complexity of this problem under various assumptions of the input parameters.

scholarly journals Using Machine Learning for Quantum Annealing Accuracy Prediction

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 187
Author(s):  
Aaron Barbosa ◽  
Elijah Pelofske ◽  
Georg Hahn ◽  
Hristo N. Djidjev
Keyword(s):  
Machine Learning ◽  
Maximum Clique ◽  
Classification Model ◽  
Maximum Clique Problem ◽  
Problem Instance ◽  
Np Hard ◽  
Machine Learning Classification ◽  
Hard Problems ◽  
Problem Instances ◽  
D Wave

Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.

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