Denotational semantics was introduced by Strachey as a means of defining semantics of programming languages. It's mathematical foundation was justified by Scott [14] in 1969 when he introduced continuous lattices to model data types and showed how to solve reflexive domain equations. It is not the case that any solution of a given reflexive domain equation is a suitable model for studying denotational semantics. In programming languages, the constructs that we deal with can all be realizable by some machines, hence their meanings, considered as mathematical objects in a lattice, should be computable. In other words, we need a solution where we can formalize the notion of computability. Of course, this means that many continuous lattices are irrelevant to the study of denotational semantics of programming languages. It is the purpose of this paper to isolate those lattices which are relevant.
{"title":"Computability theory in admissible domains","authors":"E. Sciore, A. Tang","doi":"10.1145/800133.804337","DOIUrl":"https://doi.org/10.1145/800133.804337","url":null,"abstract":"Denotational semantics was introduced by Strachey as a means of defining semantics of programming languages. It's mathematical foundation was justified by Scott [14] in 1969 when he introduced continuous lattices to model data types and showed how to solve reflexive domain equations. It is not the case that any solution of a given reflexive domain equation is a suitable model for studying denotational semantics. In programming languages, the constructs that we deal with can all be realizable by some machines, hence their meanings, considered as mathematical objects in a lattice, should be computable. In other words, we need a solution where we can formalize the notion of computability. Of course, this means that many continuous lattices are irrelevant to the study of denotational semantics of programming languages. It is the purpose of this paper to isolate those lattices which are relevant.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122692708","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}
When studying parallel computation and synchronization one is faced with the problem of modeling the simultaneous execution of processes. Although there has been a multitude of formal means for representing such problems [2, 6, 9, 10, 13, 14, 15], invariably, when all the other complexities of the models have been stripped away, the parallelism or synchronization is studied via sequences of events. In all of these studies simultaneity of events is not studied directly. Rather, it is represented by the interleaving of the separate events into sequences, and by studying properties of the set of all such sequences.
{"title":"On formulating simultaneity for studying parallelism and synchronization","authors":"Raymond E. Miller, C. Yap","doi":"10.1145/800133.804338","DOIUrl":"https://doi.org/10.1145/800133.804338","url":null,"abstract":"When studying parallel computation and synchronization one is faced with the problem of modeling the simultaneous execution of processes. Although there has been a multitude of formal means for representing such problems [2, 6, 9, 10, 13, 14, 15], invariably, when all the other complexities of the models have been stripped away, the parallelism or synchronization is studied via sequences of events. In all of these studies simultaneity of events is not studied directly. Rather, it is represented by the interleaving of the separate events into sequences, and by studying properties of the set of all such sequences.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115671550","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}
This paper describes a data structure which is useful for representing linear lists when the pattern of accesses to a list exhibits a (perhaps time-varying) locality of reference. The structure has many of the properties of the representation proposed by Guibas, McCreight, Plass, and Roberts [4], but is substantially simpler and may be practical for lists of moderate size. The analysis of our structure includes a general treatment of the worst-case node splitting caused by consecutive insertions into a 2-3 tree.
{"title":"A representation for linear lists with movable fingers","authors":"Mark R. Brown, R. Tarjan","doi":"10.1145/800133.804328","DOIUrl":"https://doi.org/10.1145/800133.804328","url":null,"abstract":"This paper describes a data structure which is useful for representing linear lists when the pattern of accesses to a list exhibits a (perhaps time-varying) locality of reference. The structure has many of the properties of the representation proposed by Guibas, McCreight, Plass, and Roberts [4], but is substantially simpler and may be practical for lists of moderate size. The analysis of our structure includes a general treatment of the worst-case node splitting caused by consecutive insertions into a 2-3 tree.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123627050","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}
This paper concerns both the complexity aspects of PA and the pragmatics of improving algorithms for dealing with restricted subcases of PA for uses such as program verification. We improve the Cooper-Presburger decision procedure and show that the improved version permits us to obtain time and space upper bounds for PA classes restricted to a bounded number of alternations of quantifiers. The improvement is one exponent less than the upper bounds for the decision problem for full PA. The pragmatists not interested in complexity bounds can read the results as substantiation of the intuitive feeling that the improvement to the Cooper-Presburger algorithm is a real, rather than ineffectual, improvement. (It can be easily shown that the bounds obtained here are not achievable using the Cooper-Presburger procedure).
{"title":"Presburger arithmetic with bounded quantifier alternation","authors":"C. R. Reddy, D. Loveland","doi":"10.1145/800133.804361","DOIUrl":"https://doi.org/10.1145/800133.804361","url":null,"abstract":"This paper concerns both the complexity aspects of PA and the pragmatics of improving algorithms for dealing with restricted subcases of PA for uses such as program verification. We improve the Cooper-Presburger decision procedure and show that the improved version permits us to obtain time and space upper bounds for PA classes restricted to a bounded number of alternations of quantifiers. The improvement is one exponent less than the upper bounds for the decision problem for full PA. The pragmatists not interested in complexity bounds can read the results as substantiation of the intuitive feeling that the improvement to the Cooper-Presburger algorithm is a real, rather than ineffectual, improvement. (It can be easily shown that the bounds obtained here are not achievable using the Cooper-Presburger procedure).","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129471561","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}
An important goal of the theory of computation is the classification of languages according to computational difficulty. Classes such as P, NP, and LOGSPACE provide a natural framework for this, though it is a fundamental open problem to demonstrate languages distinguishing them. The complete languages of Cook, Karp, and others [1-7] are candidates for such languages in the sense that, if the classes are in fact different, these languages witness the difference. We consider two questions on regular languages resembling these open problems. One of these questions concerns 2-way non-deterministic (2n) and 2-way deterministic (2d) finite automata:
{"title":"Nondeterminism and the size of two way finite automata","authors":"W. Sakoda, M. Sipser","doi":"10.1145/800133.804357","DOIUrl":"https://doi.org/10.1145/800133.804357","url":null,"abstract":"An important goal of the theory of computation is the classification of languages according to computational difficulty. Classes such as P, NP, and LOGSPACE provide a natural framework for this, though it is a fundamental open problem to demonstrate languages distinguishing them. The complete languages of Cook, Karp, and others [1-7] are candidates for such languages in the sense that, if the classes are in fact different, these languages witness the difference. We consider two questions on regular languages resembling these open problems. One of these questions concerns 2-way non-deterministic (2n) and 2-way deterministic (2d) finite automata:","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120922024","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}
We are interes£ed in the theoretical limitations of agents M which attempt to arrive at explanations for classes of phenomena in the case where M is a machine or robot. If we take a mechanistic philosophical stance, our results can also be construed as theorems in philosophy of science. To these ends we define an ind~cJt~u£ inference ma~ne ~ssentially introduced in [6]) to be an algorithmic device with no a p~o~ bounds on how much time and memory resource it shall use, which takes as its input the graph of a function: N +N an ordered pair at a time, and which, from time to time, as it's receiving its inputs, outputs computer programs. An inductive inference machine M ide~fi66 a function f ~ M fed f (in any order) outputs over time but finitely many computer programs the last of which computes (or explains) f. No restriction is made that we should be able to algorithmically determine when (if ever) M on f has output its last computer program. We say that M ide~fi~6 a ~s S of functions (or phenomena) .~ > M identifies each f in S. For example, the following proposition generalizes a remark in [2]. The notation is from [ii]: ~e is the partial function computed by program e and K in some set representing the halting problem.
{"title":"Anomaly hierarchies of mechanized inductive inference","authors":"J. Case, Carl H. Smith","doi":"10.1145/800133.804360","DOIUrl":"https://doi.org/10.1145/800133.804360","url":null,"abstract":"We are interes£ed in the theoretical limitations of agents M which attempt to arrive at explanations for classes of phenomena in the case where M is a machine or robot. If we take a mechanistic philosophical stance, our results can also be construed as theorems in philosophy of science. To these ends we define an ind~cJt~u£ inference ma~ne ~ssentially introduced in [6]) to be an algorithmic device with no a p~o~ bounds on how much time and memory resource it shall use, which takes as its input the graph of a function: N +N an ordered pair at a time, and which, from time to time, as it's receiving its inputs, outputs computer programs. An inductive inference machine M ide~fi66 a function f ~ M fed f (in any order) outputs over time but finitely many computer programs the last of which computes (or explains) f. No restriction is made that we should be able to algorithmically determine when (if ever) M on f has output its last computer program. We say that M ide~fi~6 a ~s S of functions (or phenomena) .~ > M identifies each f in S. For example, the following proposition generalizes a remark in [2]. The notation is from [ii]: ~e is the partial function computed by program e and K in some set representing the halting problem.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127327780","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 number of different models of synchronous, unbounded parallel computers have appeared in recent literature. Without exception, running time on these models has been shown to be polynomially related to the classical space complexity measure. The general applicability of this relationship is called “the parallel computation thesis” and strong evidence of its truth is given in this paper by introducing the notion of “conglomerates” - a very large class of parallel machines, including all those which could feasibly be built. Basic parallel machine models are also investigated, in an attempt to pin down the notion of parallel time to within a constant factor. To this end, a universal conglomerate structure is developed with can simulate any other basic model within linear time. This approach also leads to fair estimates of instruction execution times for various parallel models.
{"title":"A unified approach to models of synchronous parallel machines","authors":"L. Goldschlager","doi":"10.1145/800133.804336","DOIUrl":"https://doi.org/10.1145/800133.804336","url":null,"abstract":"A number of different models of synchronous, unbounded parallel computers have appeared in recent literature. Without exception, running time on these models has been shown to be polynomially related to the classical space complexity measure. The general applicability of this relationship is called “the parallel computation thesis” and strong evidence of its truth is given in this paper by introducing the notion of “conglomerates” - a very large class of parallel machines, including all those which could feasibly be built. Basic parallel machine models are also investigated, in an attempt to pin down the notion of parallel time to within a constant factor. To this end, a universal conglomerate structure is developed with can simulate any other basic model within linear time. This approach also leads to fair estimates of instruction execution times for various parallel models.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131056737","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}
Recent research has investigated time-space tradeoffs for register allocation strategies of certain fixed sets of expressions. This paper is concerned with the time-space tradeoff for register allocation strategies of any set of expressions which compute given functions. Time-space tradeoffs for pebbling superconcentrators and grates are developed. Corollaries which follow include tradeoffs for any straight-line program which computes polynomial multiplication, polynomial convolution, the discrete Fourier transform, oblivious merging, and most sets of linear forms.
{"title":"Time-space tradeoffs for computing functions, using connectivity properties of their circuits","authors":"M. Tompa","doi":"10.1145/800133.804348","DOIUrl":"https://doi.org/10.1145/800133.804348","url":null,"abstract":"Recent research has investigated time-space tradeoffs for register allocation strategies of certain fixed sets of expressions. This paper is concerned with the time-space tradeoff for register allocation strategies of any set of expressions which compute given functions. Time-space tradeoffs for pebbling superconcentrators and grates are developed. Corollaries which follow include tradeoffs for any straight-line program which computes polynomial multiplication, polynomial convolution, the discrete Fourier transform, oblivious merging, and most sets of linear forms.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134282156","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}
Fast computation of polynomials of 1 variable in the fields R and C of real and complex numbers is considered. The optimal schemes of computation with preconditioning (that is, the schemes involving the minimal number of arithmetic operations without counting preliminary treatment of coefficients) for evaluation in C are presented. The schemes which are close to optimal ones are presented for evaluation in R. The difference between the complexity of computation in R and in C is established. A new generalization of the problem is presented.
{"title":"Computational complexity of computing polynomials over the fields of real and complex numbers","authors":"V. Pan","doi":"10.1145/800133.804344","DOIUrl":"https://doi.org/10.1145/800133.804344","url":null,"abstract":"Fast computation of polynomials of 1 variable in the fields R and C of real and complex numbers is considered. The optimal schemes of computation with preconditioning (that is, the schemes involving the minimal number of arithmetic operations without counting preliminary treatment of coefficients) for evaluation in C are presented. The schemes which are close to optimal ones are presented for evaluation in R. The difference between the complexity of computation in R and in C is established. A new generalization of the problem is presented.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117013015","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 classical problem in concurrent program control is to provide a mechanism whereby several processes running concurrently can gain exclusive control of a resource. For each process, the section of its program in which it accesses the resource is called its critical section, and the problem is called the critical section problem. A solution to the critical section problem guarantees that no more than one process can be in its critical section at any time. The solution presented here improves on previous solutions by allowing processes to enter their critical sections on a first-come first-served basis.
{"title":"A new solution to the critical section problem","authors":"H. Katseff","doi":"10.1145/800133.804335","DOIUrl":"https://doi.org/10.1145/800133.804335","url":null,"abstract":"A classical problem in concurrent program control is to provide a mechanism whereby several processes running concurrently can gain exclusive control of a resource. For each process, the section of its program in which it accesses the resource is called its critical section, and the problem is called the critical section problem. A solution to the critical section problem guarantees that no more than one process can be in its critical section at any time. The solution presented here improves on previous solutions by allowing processes to enter their critical sections on a first-come first-served basis.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121081498","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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