ion ● Approximation ○ M’ approximates M ○ Use M’ to deduce properties of M
{"title":"Model Checking","authors":"Zhenhua Duan, Cong Tian","doi":"10.1201/b13055-18","DOIUrl":"https://doi.org/10.1201/b13055-18","url":null,"abstract":"ion ● Approximation ○ M’ approximates M ○ Use M’ to deduce properties of M","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"1 1","pages":"337-369"},"PeriodicalIF":0.0,"publicationDate":"2019-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124273697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite Automata Minimization","authors":"Marco Almeida, Nelma Moreira, Rogério Reis","doi":"10.1201/b13055-8","DOIUrl":"https://doi.org/10.1201/b13055-8","url":null,"abstract":"","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122586512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum Finite Automata","authors":"Daowen Qiu, Lvzhou Li, P. Mateus, J. Gruska","doi":"10.1201/b13055-7","DOIUrl":"https://doi.org/10.1201/b13055-7","url":null,"abstract":"","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129715275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Petri Nets (PN's) is a formal and graphical appealing language which is appropriate for modeling systems with concurrency. PN's has been under development since the beginning of the 60'ies, when Carl Adam Petri defined the language. It was the first time a general theory for discrete parallel systems was formulated. Description of a PN model. The language is a generalization of automata theory such that the concept of concurrently occurring events can be expressed. PN model is oriented to the description of both states of a system and actions producing evolution through the states. In this sense, it differs from other formal models of concurrent systems which usually are state-based or action-based. PN's treat states and actions on equal footing. In fact, the structure of a PN can be seen as a bipartite graph whose two different kind of nodes, places and transitions, correspond with states and actions of the system. Certain similarity with queueing models can be observed at this point. Storage rooms and service stations of queueing networks represent also states and actions, respectively. In queueing models the state of the system is represented by means of a given distribution of customers at storage rooms (queues). In an analogous way, a marking or distribution of tokens (marks) over the places of the PN defines the state of the system. Therefore, as for queueing networks, the representation of a state is distributed (see Figure 1.a). The behavior of a queueing network is governed by the departures of customers from stations, after finishing service, and the movement towards other storage rooms. The token game is the analogue in PN models. Tokens are stored at places and the firing of a transition produces a change of the distribution of tokens or new marking (see Figure 1.b). Adequacy of the paradigm. The first main property of PN models for the description of concurrent systems is its simplicity. A very few and simple mathematical entities are necessary for the formal definition of nets. This fact constitute a great advantage, mainly in the modeling of concurrent systems which are enough complicated per se. In spite of the simplicity of the model, its generality must be remarked. The three basic schemes in the modeling of concurrent systems can be included in the PN structure: sequencing, choice, and concurrency. Moreover, other typical and well-known elements in the modeling of distributed systems, as rendezvous , shared resources, …
{"title":"Petri Nets","authors":"Jean-Marie Proth","doi":"10.1201/b13055-16","DOIUrl":"https://doi.org/10.1201/b13055-16","url":null,"abstract":"Petri Nets (PN's) is a formal and graphical appealing language which is appropriate for modeling systems with concurrency. PN's has been under development since the beginning of the 60'ies, when Carl Adam Petri defined the language. It was the first time a general theory for discrete parallel systems was formulated. Description of a PN model. The language is a generalization of automata theory such that the concept of concurrently occurring events can be expressed. PN model is oriented to the description of both states of a system and actions producing evolution through the states. In this sense, it differs from other formal models of concurrent systems which usually are state-based or action-based. PN's treat states and actions on equal footing. In fact, the structure of a PN can be seen as a bipartite graph whose two different kind of nodes, places and transitions, correspond with states and actions of the system. Certain similarity with queueing models can be observed at this point. Storage rooms and service stations of queueing networks represent also states and actions, respectively. In queueing models the state of the system is represented by means of a given distribution of customers at storage rooms (queues). In an analogous way, a marking or distribution of tokens (marks) over the places of the PN defines the state of the system. Therefore, as for queueing networks, the representation of a state is distributed (see Figure 1.a). The behavior of a queueing network is governed by the departures of customers from stations, after finishing service, and the movement towards other storage rooms. The token game is the analogue in PN models. Tokens are stored at places and the firing of a transition produces a change of the distribution of tokens or new marking (see Figure 1.b). Adequacy of the paradigm. The first main property of PN models for the description of concurrent systems is its simplicity. A very few and simple mathematical entities are necessary for the formal definition of nets. This fact constitute a great advantage, mainly in the modeling of concurrent systems which are enough complicated per se. In spite of the simplicity of the model, its generality must be remarked. The three basic schemes in the modeling of concurrent systems can be included in the PN structure: sequencing, choice, and concurrency. Moreover, other typical and well-known elements in the modeling of distributed systems, as rendezvous , shared resources, …","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132912166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rozdzial przedstawia algorytmy przyrostowego i polprzyrostowego tworzenia minimalnych deterministycznych automatow skonczonych.
{"title":"Incremental Construction of Finite-State Automata","authors":"J. Daciuk","doi":"10.1201/b13055-9","DOIUrl":"https://doi.org/10.1201/b13055-9","url":null,"abstract":"Rozdzial przedstawia algorytmy przyrostowego i polprzyrostowego tworzenia minimalnych deterministycznych automatow skonczonych.","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124652599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A relation is a set of pairs—in this paper, a subset of ⌃⇤ ⇥ ⇤, so it relates strings over an “input” alphabet ⌃ to strings over an “output” alphabet . A weighted relation is a function R that maps any string pair (x,y) to a weight in R 0. We say that the relation R is rational if R can be defined by some weighted finite-state transducer (FST) T . As formalized in Appendix A.3, this means thatR(x,y) is the total weight of all accepting paths in T that are labeled with (x,y) (which is 0 if there are no such accepting paths). The weight of each accepting path in T is given by the product of its arc weights, which fall in R>0. The set of pairs support(R) , {(x,y) : R(x,y) > 0} is then said to be a regular relation because it is recognized by the unweighted FST obtained by dropping the weights from T . In this paper, we are interested in defining non-rational weighting functions R with this same regular support set.
{"title":"Finite State Transducers","authors":"J. Baliosian, Dina Wonsever","doi":"10.1201/b13055-4","DOIUrl":"https://doi.org/10.1201/b13055-4","url":null,"abstract":"A relation is a set of pairs—in this paper, a subset of ⌃⇤ ⇥ ⇤, so it relates strings over an “input” alphabet ⌃ to strings over an “output” alphabet . A weighted relation is a function R that maps any string pair (x,y) to a weight in R 0. We say that the relation R is rational if R can be defined by some weighted finite-state transducer (FST) T . As formalized in Appendix A.3, this means thatR(x,y) is the total weight of all accepting paths in T that are labeled with (x,y) (which is 0 if there are no such accepting paths). The weight of each accepting path in T is given by the product of its arc weights, which fall in R>0. The set of pairs support(R) , {(x,y) : R(x,y) > 0} is then said to be a regular relation because it is recognized by the unweighted FST obtained by dropping the weights from T . In this paper, we are interested in defining non-rational weighting functions R with this same regular support set.","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130263867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite State Automata in Compilers","authors":"Yang Zhao","doi":"10.1201/b13055-14","DOIUrl":"https://doi.org/10.1201/b13055-14","url":null,"abstract":"","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127941358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Most machine models one studies in theoretical computer science, like Turing machines and finite automata, work on inputs that are strings over some finite alphabet. However, often problem descriptions have inputs that more structured than strings. For example, the input could be a graph, or a tree, or a partial order, etc. We will now introduce an automaton model that computes on inputs that are trees.
{"title":"Tree Automata","authors":"Olivier Gauwin","doi":"10.1201/b13055-5","DOIUrl":"https://doi.org/10.1201/b13055-5","url":null,"abstract":"Most machine models one studies in theoretical computer science, like Turing machines and finite automata, work on inputs that are strings over some finite alphabet. However, often problem descriptions have inputs that more structured than strings. For example, the input could be a graph, or a tree, or a partial order, etc. We will now introduce an automaton model that computes on inputs that are trees.","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"376 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131725004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Various quantum versions o f the most basic models o f the classical finite automata have already been introduced and various modes of their computations have already started t o be investigated. In this paper we overview basic models, approaches, techniques and results in this promising area of quantum automata that is expected to play an important role also in theoretical computer science. We also summarize some open problems and research directions to pursue in this area.
{"title":"Regular Path Queries on Graph-Structured Data","authors":"Alex Thomo, Venkatesh Srinivasan","doi":"10.1201/b13055-11","DOIUrl":"https://doi.org/10.1201/b13055-11","url":null,"abstract":"Various quantum versions o f the most basic models o f the classical finite automata have already been introduced and various modes of their computations have already started t o be investigated. In this paper we overview basic models, approaches, techniques and results in this promising area of quantum automata that is expected to play an important role also in theoretical computer science. We also summarize some open problems and research directions to pursue in this area.","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123600879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Statecharts","authors":"Hanlin Lu, Sheng Yu","doi":"10.1201/b13055-17","DOIUrl":"https://doi.org/10.1201/b13055-17","url":null,"abstract":"","PeriodicalId":302611,"journal":{"name":"Handbook of Finite State Based Models and Applications","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134479658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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