arXiv subjects

Khaled El-Fakih

Publications and source records attributed to Khaled El-Fakih.

3 recordsLinked to original sources

arXiv2026

A quantum model for synchronizing finite state transition systems

We propose a quantum model for finding a resetting input sequence (RS) which can take a finite state transition system (FA), to particular state independent of its current state. The complexity of finding such sequences for various types of FA can be NP-Hard or even PSPACE-Complete. To this end, we represent the FA states, inputs, and transition function in quantum space. Accordingly, we propose a model to represent the execution of an input sequence of a particular length $l$ starting form an initial FA state. The model is extended considering the application in superposition of all input sequences of length $l$ to an initial state of the FA. The model is further extended considering the application of all input sequences to all initial states of the FA capturing for every input sequence the collection (ordered list) of states reached by applying the sequence to all states of the FA. The amplitude amplification algorithm is then used as it combines similar collections of reached states while preserving all input sequences that reach these collections. A Grover search for a reached collection where its elements correspond to the same FA state provides a RS for the FA. Our approach offers a quadratic gain over the exponential complexity of traditional brute-force method, which is the only method that can be applied to a general FA class. As a proof of concept we provide results of several simulated FAs on a quantum simulator.

quant-ph↗

arXiv2021

Equivalence Checking and Intersection of Deterministic Timed Finite State Machines

There has been a growing interest in defining models of automata enriched with time, such as finite automata extended with clocks (timed automata). In this paper, we study deterministic timed finite state machines (TFSMs), i.e., finite state machines with a single clock, timed guards and timeouts which transduce timed input words into timed output words. We solve the problem of equivalence checking by defining a bisimulation from timed FSMs to untimed ones and viceversa. Moreover, we apply these bisimulation relations to build the intersection of two timed finite state machines by untiming them, intersecting them and transforming back to the timed intersection.

cs.FL↗

arXiv2014

Deterministic Timed Finite State Machines: Equivalence Checking and Expressive Power

There has been a growing interest in defining models of automata enriched with time. For instance, timed automata were introduced as automata extended with clocks. In this paper, we study models of timed finite state machines (TFSMs), i.e., FSMs enriched with time, which accept timed input words and generate timed output words. Here we discuss some models of TFSMs with a single clock: TFSMs with timed guards, TFSMs with timeouts, and TFSMs with both timed guards and timeouts. We solve the problem of equivalence checking for all three models, and we compare their expressive power, characterizing subclasses of TFSMs with timed guards and of TFSMs with timeouts that are equivalent to each other.

cs.FL↗