[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83166-en":3,"doc-seo-83166-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83166,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","A Quantum Model for Synchronizing Finite State Transition Systems","A quantum model is proposed for finding a resetting input sequence (RS) that drives a finite state transition system (FA) into a particular state independent of its current state. For several FA classes, the task can be NP-Hard or even PSPACE-Complete. The approach encodes FA states, inputs, and the transition function in quantum space, models executions for input sequences of length l, and extends to superpositions over all sequences and all initial states. Amplitude amplification and Grover search locate reached state collections to produce an RS, offering quadratic improvement over brute force; simulated FA results validate the concept.","arXiv :2607 .06953v1 [ quant-ph] 8 Jul 2026  \nA quantum model for synchronizing finite state transition systems  \nMartin Lukac 1 , Khaled El-Fakih2 , and Uraz Cengiz T¨urker3  \n1 Hiroshima City University, Hiroshima, Japan, [malu@hiroshima-cu.ac.jp](malu@hiroshima-cu.ac.jp)  \n2 Aemerican University of Sharjah, Sharjah, UAE, [kelfakih@aus.edu](kelfakih@aus.edu)  \n3 University of Lancaster, Lancaster, UK, [u.turker@lancaster.ac.uk](u.turker@lancaster.ac.uk)  \nAbstract  \nWe 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, werepresent 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.  \n1 Introduction  \nState transition-based systems are an umbrella term to represent systems that change their internal states after receiving some inputs. These systems include, but are not limited to, hardware, software, mathematical, and biological systems. In general, state-transition-based systems must return to a particular initial (or consistent/safe) state to function correctly. This operation is known as the reset operation. In essence areset operation defines the steps required to bring the system back to a particular initial or consistent state independent of its current state. Because of its role, resets are indispensable aspects of many systems. Some systems use reset circuits to carry out this operation. In case of lack of reset circuits, a reset operation is done by executing a sequence of inputs called reset sequence (RS) (also named as synchronizing sequence ora reset word) .  \nIn robotics, for example, RSs are crucial for multi-robot manipulation and transportation, where multiple robots must coordinate and recover from faults to ensure the system operates smoothly [1] .  \nAutomotive control systems also benefit from these sequences, as they help synchronize embedded systems in vehicles, maintaining safety and functionality in critical systems after unexpected failures [9] .  \nIn communication systems, RSs ensure the synchronization of protocol handlers after disruptions, enabling uninterrupted data flow and maintaining the integrity of communication networks [21] .  \nRSs are also key in software engineering; namely, in conformance testing of reactive systems where many tests or input words are derived to detect errors or unexpected behaviour of a given implementation. The implementation needs to be reset before running each test [8, 25, 20] .  \nIn bio-computing, a collection of automata work in parallel on different inputs and in order to start a new computation a RS is applied to reset the automata to their initial states. In [4] for example, the  \nresearchers showed that in a controlled environment they ran 3 ∗ 1012 automata pe","cbCaifN31wiqOYBX","https://ap.wps.com/l/cbCaifN31wiqOYBX","pdf",353488,3,1,18,"English","en",105,"# Introduction\n## Reset operations and reset sequences\n## Finite automata and classes\n## Computational complexity of finding reset sequences","[{\"question\":\"What problem does the document address?\",\"answer\":\"It addresses how to find a resetting input sequence (RS) that synchronizes a finite state transition system (finite automaton) to a target state regardless of the system’s current state.\"},{\"question\":\"Why is the RS-finding problem computationally difficult?\",\"answer\":\"The document states that for various FA types, finding such sequences can be NP-Hard and the decision variants can reach PSPACE-Complete, making general-purpose solutions hard.\"},{\"question\":\"How does the proposed quantum approach improve over brute force?\",\"answer\":\"It represents states, inputs, and transitions in quantum space, uses superpositions over sequences and initial states, and applies amplitude amplification to combine reached state collections, then uses Grover search to identify a collection yielding an RS, giving a quadratic gain over exponential brute-force 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problem does the document address?","Question",{"text":75,"@type":76},"It addresses how to find a resetting input sequence (RS) that synchronizes a finite state transition system (finite automaton) to a target state regardless of the system’s current state.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is the RS-finding problem computationally difficult?",{"text":80,"@type":76},"The document states that for various FA types, finding such sequences can be NP-Hard and the decision variants can reach PSPACE-Complete, making general-purpose solutions hard.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed quantum approach improve over brute force?",{"text":84,"@type":76},"It represents states, inputs, and transitions in quantum space, uses superpositions over sequences and initial states, and applies amplitude amplification to combine reached state collections, then uses Grover search to identify a collection yielding an RS, giving a quadratic gain over 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