{"id":148019,"date":"2008-01-01T00:00:00","date_gmt":"2008-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/a-chart-semantics-for-the-pi-calculus\/"},"modified":"2018-10-16T20:00:53","modified_gmt":"2018-10-17T03:00:53","slug":"a-chart-semantics-for-the-pi-calculus","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/a-chart-semantics-for-the-pi-calculus\/","title":{"rendered":"A Chart Semantics for the Pi-calculus"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We present a graphical semantics for the pi-calculus, that is easier to visualize and better suited to expressing causality and temporal properties than conventional relational semantics. A pi-chart is a finite directed acyclic graph recording a computation in the pi-calculus. Each node represents a process, and each edge either represents a computation step, or a message-passing interaction. Pi-charts enjoy a natural pictorial representation, akin to message sequence charts, in which vertical edges represent control flow and horizontal edges represent data flow based on message passing. A pi-chart represents a single computation starting from its top (the nodes with no ancestors) to its bottom (the nodes with no descendants). Unlike conventional reductions or transitions, the edges in a pi-chart induce ancestry and other causal relations on processes. We give both compositional and operational definitions of pi-charts, and illustrate the additional expressivity afforded by the chart semantics via a series of examples.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present a graphical semantics for the pi-calculus, that is easier to visualize and better suited to expressing causality and temporal properties than conventional relational semantics. A pi-chart is a finite directed acyclic graph recording a computation in the pi-calculus. Each node represents a process, and each edge either represents a computation step, or a [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Elsevier","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"2","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Electronic Notes in Theoretical Computer Science","msr_number":"","msr_organization":"","msr_pages_string":"3-29","msr_page_range_start":"3","msr_page_range_end":"29","msr_series":"","msr_volume":"194","msr_copyright":"","msr_conference_name":"","msr_doi":"doi:10.1016\/j.entcs.2007.11.002","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2008-01-16","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":2008,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13546],"msr-publication-type":[193715],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-148019","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"Elsevier","msr_edition":"","msr_affiliation":"","msr_published_date":"2008-01-16","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"3-29","msr_chapter":"2","msr_isbn":"","msr_journal":"Electronic Notes in Theoretical Computer Science","msr_volume":"194","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"226042","msr_publicationurl":"","msr_doi":"doi:10.1016\/j.entcs.2007.11.002","msr_publication_uploader":[{"type":"file","title":"ENTCS08.pdf","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2008\/01\/ENTCS08.pdf","id":226042,"label_id":0},{"type":"doi","title":"doi:10.1016\/j.entcs.2007.11.002","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[{"id":226042,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2008\/01\/ENTCS08.pdf"}],"msr-author-ordering":[{"type":"text","value":"Johannes Borgstr\u00f6m","user_id":0,"rest_url":false},{"type":"user_nicename","value":"adg","user_id":30825,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=adg"},{"type":"user_nicename","value":"aphillip","user_id":31075,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=aphillip"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[170002],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"article","related_content":{"projects":[{"ID":170002,"post_title":"Stochastic Pi Machine","post_name":"stochastic-pi-machine","post_type":"msr-project","post_date":"2008-11-21 03:48:26","post_modified":"2020-03-06 10:54:09","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/stochastic-pi-machine\/","post_excerpt":"The Stochastic Pi Machine (SPiM) is a programming language for designing and simulating computer models of biological processes. The language is based on a mathematical formalism known as the pi-calculus, and the simulation algorithm is based on standard kinetic theory of physical chemistry. The language features a simple graphical notation for modelling a range of biological systems, and can be used to model large systems incrementally, by directly composing simpler models of subsystems","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/170002"}]}}]},"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/148019","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/148019\/revisions"}],"predecessor-version":[{"id":518536,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/148019\/revisions\/518536"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=148019"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=148019"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=148019"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=148019"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=148019"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=148019"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=148019"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=148019"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=148019"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=148019"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=148019"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=148019"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=148019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}