{"title":"On the Complexity of Szilard Languages of Matrix Grammars","authors":"Liliana Cojocaru, E. Mäkinen","doi":"10.1109/SYNASC.2011.34","DOIUrl":null,"url":null,"abstract":"We investigate computational resources used by alternating Turing machines (ATMs) to accept Szilard languages (SZLs) of context-free matrix grammars (MGs). The main goal is to relate these languages to parallel complexity classes such as NC1 and NC2. We prove that unrestricted and leftmost-1 SZLs of context-free MGs, without appearance checking, can be accepted by ATMs in logarithmic time and space. Hence, these classes of languages belong to NC1 (under ALOGTIME reduction). Unrestricted SZLs of context-free MGs with appearance checking can be accepted by ATMs in logarithmic space and square logarithmic time. Consequently, this class is contained in NC2. We conclude with some results on SZLs of MGs with phrase-structure rules.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2011.34","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
We investigate computational resources used by alternating Turing machines (ATMs) to accept Szilard languages (SZLs) of context-free matrix grammars (MGs). The main goal is to relate these languages to parallel complexity classes such as NC1 and NC2. We prove that unrestricted and leftmost-1 SZLs of context-free MGs, without appearance checking, can be accepted by ATMs in logarithmic time and space. Hence, these classes of languages belong to NC1 (under ALOGTIME reduction). Unrestricted SZLs of context-free MGs with appearance checking can be accepted by ATMs in logarithmic space and square logarithmic time. Consequently, this class is contained in NC2. We conclude with some results on SZLs of MGs with phrase-structure rules.
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