We present a systematic way of studying state machine based design spaces and apply it to the study of asynchronous pipelines. Starting with the specification of the most concurrent behaviour as a state machine, all possible valid smaller designs may be generated by systematically removing structured patterns of output states (C cuts) and input states (R cuts). Taking the cartesian product of cuts C×R yields the complete design space which may then be partitioned according to well understood design styles. In this paper we extend previous results by studying mixed asynchronous pipelines of which homogeneous behaviours form a subset. The approach is presented using the much smaller 2phase setting (3×6) but the insights and structures revealed carry over to full 4phase designs (35×140). We present a complete overview of mixed 2phase linear pipeline behaviours; show how their structuring C cuts and R cuts relate; characterise the behaviours of linear pipelines in terms of these cuts for any depth; and show how the much larger R mixed behaviour patterns can be calculated from knowledge of the C behaviour patterns. Applications of the theory cover mixed linear pipeline and ring behaviours and the automatic generation of quality circuits from our specifications.
{"title":"A Design Space and its Patterns: Modelling 2phase Asynchronous Pipelines","authors":"G. Birtwistle, K. Stevens","doi":"10.29007/8p8h","DOIUrl":"https://doi.org/10.29007/8p8h","url":null,"abstract":"We present a systematic way of studying state machine based design spaces and apply it to the study of asynchronous pipelines. Starting with the specification of the most concurrent behaviour as a state machine, all possible valid smaller designs may be generated by systematically removing structured patterns of output states (C cuts) and input states (R cuts). Taking the cartesian product of cuts C×R yields the complete design space which may then be partitioned according to well understood design styles. In this paper we extend previous results by studying mixed asynchronous pipelines of which homogeneous behaviours form a subset. The approach is presented using the much smaller 2phase setting (3×6) but the insights and structures revealed carry over to full 4phase designs (35×140). We present a complete overview of mixed 2phase linear pipeline behaviours; show how their structuring C cuts and R cuts relate; characterise the behaviours of linear pipelines in terms of these cuts for any depth; and show how the much larger R mixed behaviour patterns can be calculated from knowledge of the C behaviour patterns. Applications of the theory cover mixed linear pipeline and ring behaviours and the automatic generation of quality circuits from our specifications.","PeriodicalId":422904,"journal":{"name":"HOWARD-60","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":"125963139","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}
In this note, we consider a notion of minimum model suitable for formulating a semantics of evolvable computing systems using a revision-based logic. We explore a range of proof systems for reasoning in the logic of minimum models and consider their application to the simulation of evolvable systems. Finally, we outline how these proof systems may be implemented in a logical framework.
{"title":"A note on first-order reasoning for minimum models","authors":"D. Rydeheard, Jesús Héctor Domínguez Sánchez","doi":"10.29007/5bvp","DOIUrl":"https://doi.org/10.29007/5bvp","url":null,"abstract":"In this note, we consider a notion of minimum model suitable for formulating a semantics of evolvable computing systems using a revision-based logic. We explore a range of proof systems for reasoning in the logic of minimum models and consider their application to the simulation of evolvable systems. Finally, we outline how these proof systems may be implemented in a logical framework.","PeriodicalId":422904,"journal":{"name":"HOWARD-60","volume":"521 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":"116704334","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}
Model checking and runtime verification are pillars of formal verification but for the most part are used independently. In this position paper we argue that the formal verification community would be well-served by developing theory, algorithms, implementations, and applications that combine model checking and runtime verification into a single, seamless technology. This technology would allow system developers to carefully choose the appropriate balance between offline verification of expressive properties (model checking) and online verification of important parts of the system’s state space (runtime verification). We present several realistic examples where such technology appears necessary and a preliminary formalization of the idea.
{"title":"Model Check What You Can, Runtime Verify the Rest","authors":"Timothy L. Hinrichs, A. Sistla, L. Zuck","doi":"10.29007/slnn","DOIUrl":"https://doi.org/10.29007/slnn","url":null,"abstract":"Model checking and runtime verification are pillars of formal verification but for the most part are used independently. In this position paper we argue that the formal verification community would be well-served by developing theory, algorithms, implementations, and applications that combine model checking and runtime verification into a single, seamless technology. This technology would allow system developers to carefully choose the appropriate balance between offline verification of expressive properties (model checking) and online verification of important parts of the system’s state space (runtime verification). We present several realistic examples where such technology appears necessary and a preliminary formalization of the idea.","PeriodicalId":422904,"journal":{"name":"HOWARD-60","volume":"149 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":"121773513","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}
How do we engage with the artefacts that we build as software engineers or computer scientists? Programs are one thing: we can execute them and see how they behave, as well as engaging with them in other ways. Other artefacts – many of which are more abstract and formal – present more of a problem. Mathematicians, who are used to dealing with rigorously presented ideas and proofs, have a social process for dealing with understanding. Arguably, however, they have just the same problem with a more formal presentation: for example, by all accounts Russell and Whitehead’s Principia Mathematica is riddled with mistakes of minor and more major significance. In the computing domain, what sort of questions do we want to ask about an artefact such as a specification or a set of tests?
{"title":"Extended Abstract: Getting Engaged","authors":"S. Thompson","doi":"10.29007/8h8t","DOIUrl":"https://doi.org/10.29007/8h8t","url":null,"abstract":"How do we engage with the artefacts that we build as software engineers or computer scientists? Programs are one thing: we can execute them and see how they behave, as well as engaging with them in other ways. Other artefacts – many of which are more abstract and formal – present more of a problem. Mathematicians, who are used to dealing with rigorously presented ideas and proofs, have a social process for dealing with understanding. Arguably, however, they have just the same problem with a more formal presentation: for example, by all accounts Russell and Whitehead’s Principia Mathematica is riddled with mistakes of minor and more major significance. In the computing domain, what sort of questions do we want to ask about an artefact such as a specification or a set of tests?","PeriodicalId":422904,"journal":{"name":"HOWARD-60","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":"127220323","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}
The Talmud is a body of arguments and discussions about all aspects of the human agent’s social, legal and religious life. It was completed over 1500 years ago and its argumentation and debates contain many logical principles and examples very much relevant to today’s research in logic, artificial intelligence, law and argumentation. In a series of books on Talmudic Logic, the authors have studied the logical prinicples involved in the Talmud, one by one, devoting a volume to each major principle We have just finished writing Volume 5, entitled Resolution of Conflicts and Normative Loops in the Talmud, and the present paper describes how the Talmud deals with even and odd loops and compares the results with open issues in argumentation. For other English papers corresponding to previous books, see [1, 2, 3, 4, 5, 6]. We start by looking at two typical loops, as in Figures 1 and 2.
{"title":"The Handling of Loops in Talmudic Logic, with Application to Odd and Even Loops in Argumentation","authors":"M. Abraham, D. Gabbay, U. Schild","doi":"10.29007/gkg6","DOIUrl":"https://doi.org/10.29007/gkg6","url":null,"abstract":"The Talmud is a body of arguments and discussions about all aspects of the human agent’s social, legal and religious life. It was completed over 1500 years ago and its argumentation and debates contain many logical principles and examples very much relevant to today’s research in logic, artificial intelligence, law and argumentation. In a series of books on Talmudic Logic, the authors have studied the logical prinicples involved in the Talmud, one by one, devoting a volume to each major principle We have just finished writing Volume 5, entitled Resolution of Conflicts and Normative Loops in the Talmud, and the present paper describes how the Talmud deals with even and odd loops and compares the results with open issues in argumentation. For other English papers corresponding to previous books, see [1, 2, 3, 4, 5, 6]. We start by looking at two typical loops, as in Figures 1 and 2.","PeriodicalId":422904,"journal":{"name":"HOWARD-60","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":"122908480","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}
Up and Down the Temporal Way” was a paper published by Howard Barringer in the 1980s that used temporal logics to formally specify a lift system. Based on that temporal specification, we describe some advances and extensions to temporal specification and verification that the authors have been involved with since then.
{"title":"On and On the Temporal Way","authors":"C. Dixon, Michael Fisher","doi":"10.29007/sz8j","DOIUrl":"https://doi.org/10.29007/sz8j","url":null,"abstract":"Up and Down the Temporal Way” was a paper published by Howard Barringer in the 1980s that used temporal logics to formally specify a lift system. Based on that temporal specification, we describe some advances and extensions to temporal specification and verification that the authors have been involved with since then.","PeriodicalId":422904,"journal":{"name":"HOWARD-60","volume":"72 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":"127956237","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 present a sound and complete model theory for theories of β-reduction with or without η-expansion. We then show in what conditions we obtain models of β-equality and βη-equality.
{"title":"A simple and complete model theory for intensional and extensional untyped λ-equality","authors":"M. Gabbay","doi":"10.29007/2vzl","DOIUrl":"https://doi.org/10.29007/2vzl","url":null,"abstract":"We present a sound and complete model theory for theories of β-reduction with or without η-expansion. We then show in what conditions we obtain models of β-equality and βη-equality.","PeriodicalId":422904,"journal":{"name":"HOWARD-60","volume":"20 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":"127820860","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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