Efficient state reduction methods for PLA-based sequential circuits

Experiences with heuristics for the state reduction of finite-state machines are presented and two new heuristic algorithms described in detail. Results on machines from the literature and from the MCNC benchmark set are shown. The area of the PLA implementation of the combinational component and the design time are used as figures of merit. The comparison of such parameters, when the state reduction step is included in the design process and when it is not, suggests that fast state-reduction heuristics should be implemented within FSM automatic synthesis systems

A sufficient condition to polynomially compute a minimum separating DFA

This is the author’s version of a work that was accepted for publication in Information Sciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information Sciences 370–371 (2016) 204–220. DOI 10.1016/j.ins.2016.07.053.The computation of a minimal separating automaton (MSA) for regular languages has been studied from many different points of view, from synthesis of automata or Grammatical Inference to the minimization of incompletely specified machines or Compositional Verification. In the general case, the problem is NP-complete, but this drawback does not prevent the problem from having a real application in the above-mentioned fields. In this paper, we propose a sufficient condition that guarantees that the computation of the MSA can be carried out with polynomial time complexity. © 2016 Elsevier Inc. All rights reserved.Vázquez-De-Parga Andrade, M.; García Gómez, P.; López Rodríguez, D. (2016). A sufficient condition to polynomially compute a minimum separating DFA. Information Sciences. 370-371:204-220. doi:10.1016/j.ins.2016.07.053S204220370-37

Optimal state reductions of automata with partially specified behaviors

Nondeterministic finite automata with don't care states, namely states which neither accept nor reject, are considered. A characterization of deterministic automata compatible with such a device is obtained. Furthermore, an optimal state bound for the smallest compatible deterministic automata is provided. It is proved that the problem of minimizing deterministic don't care automata is NP-complete and PSPACE-hard in the nondeterministic case. The restriction to the unary case is also considered

A QUANTUM ALGORITHM FOR AUTOMATA ENCODING

Encoding of finite automata or state machines is critical to modern digital logic design methods for sequential circuits. Encoding is the process of assigning to every state, input value, and output value of a state machine a binary string, which is used to represent that state, input value, or output value in digital logic. Usually, one wishes to choose an encoding that, when the state machine is implemented as a digital logic circuit, will optimize some aspect of that circuit. For instance, one might wish to encode in such a way as to minimize power dissipation or silicon area. For most such optimization objectives, no method to find the exact solution, other than a straightforward exhaustive search, is known. Recent progress towards producing a quantum computer of large enough scale to surpass modern supercomputers has made it increasingly relevant to consider how quantum computers may be used to solve problems of practical interest. A quantum computer using Grover’s well-known search algorithm can perform exhaustive searches that would be impractical on a classical computer, due to the speedup provided by Grover’s algorithm. Therefore, we propose to use Grover’s algorithm to find optimal encodings for finite state machines via exhaustive search. We demonstrate the design of quantum circuits that allow Grover’s algorithm to be used for this purpose. The quantum circuit design methods that we introduce are potentially applicable to other problems as well

Learning Linear Temporal Properties

We present two novel algorithms for learning formulas in Linear Temporal Logic (LTL) from examples. The first learning algorithm reduces the learning task to a series of satisfiability problems in propositional Boolean logic and produces a smallest LTL formula (in terms of the number of subformulas) that is consistent with the given data. Our second learning algorithm, on the other hand, combines the SAT-based learning algorithm with classical algorithms for learning decision trees. The result is a learning algorithm that scales to real-world scenarios with hundreds of examples, but can no longer guarantee to produce minimal consistent LTL formulas. We compare both learning algorithms and demonstrate their performance on a wide range of synthetic benchmarks. Additionally, we illustrate their usefulness on the task of understanding executions of a leader election protocol

Deciding minimal distinguishing DFAs is NP-complete

In this paper, we present a proof of the NP-completeness of computing the smallest Deterministic Finite Automaton (DFA) that distinguishes two given regular languages as DFAs. A distinguishing DFA is an automaton that recognizes a language which is a subset of exactly one of the given languages. We establish the NP-hardness of this decision problem by providing a reduction from the Boolean Satisfiability Problem (SAT) to deciding the existence of a distinguishing automaton of a specific size

Quantum Algorithms for Unate and Binate Covering Problems with Application to Finite State Machine Minimization

Covering problems find applications in many areas of computer science and engineering, such that numerous combinatorial problems can be formulated as covering problems. Combinatorial optimization problems are generally NPhard problems that require an extensive search to find the optimal solution. Exploiting the benefits of quantum computing, we present a quantum oracle design for covering problems, taking advantage of Grover’s search algorithm to achieve quadratic speedup. This paper also discusses applications of the quantum counter in unate covering problems and binate covering problems with some important practical applications, such as finding prime implicants of a Boolean function, implication graphs, and minimization of incompletely specified Finite State Machines