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21
CCS with Hennessy’s merge has no finite equational axiomatization
 Theoretical Computer Science
, 2005
"... This paper confirms a conjecture of Bergstra and Klop’s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner’s Calculus of Communicationg Systems is not finitely based modulo bisimulation equ ..."
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Cited by 19 (16 self)
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This paper confirms a conjecture of Bergstra and Klop’s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner’s Calculus of Communicationg Systems is not finitely based modulo bisimulation equivalence. Thus Hennessy’s merge cannot replace the left merge and communication merge operators proposed by Bergstra and Klop, at least if a finite axiomatization of parallel composition is desired.
SOS formats and metatheory: 20 years after
, 2007
"... In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical ..."
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Cited by 10 (5 self)
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In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical
Generic trace theory
 International Workshop on Coalgebraic Methods in Computer Science (CMCS 2006), volume 164 of Elect. Notes in Theor. Comp. Sci
, 2006
"... Trace semantics has been defined for various nondeterministic systems with different input/output types, or with different types of “nondeterminism ” such as classical nondeterminism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms ..."
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Cited by 9 (4 self)
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Trace semantics has been defined for various nondeterministic systems with different input/output types, or with different types of “nondeterminism ” such as classical nondeterminism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms of “trace semantics” are instances of a single categorical construction, namely coinduction in a Kleisli category. This claim is based on our main technical result that an initial algebra in
A Hierarchy of SOS Rule Formats
, 2005
"... In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [62]. Subsequently, the format of SOS rules became the object of study. Using socalled Transition System Specifications (TS ..."
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Cited by 6 (1 self)
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In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [62]. Subsequently, the format of SOS rules became the object of study. Using socalled Transition System Specifications (TSS’s) several authors syntactically restricted the format of rules and showed several useful properties about the semantics induced by any TSS adhering to the format. This has resulted in a line of research proposing several syntactical rule formats and associated metatheorems. Properties that are guaranteed by such rule formats range from welldefinedness of the operational semantics and compositionality of behavioral equivalences to security and probabilityrelated issues. In this paper, we provide an initial hierarchy of SOS rules formats and metatheorems formulated around them.
A syntactic commutativity format for SOS
 Information Processing Letters
, 2005
"... Considering operators defined using Structural Operational Semantics (SOS), commutativity axioms are intuitive properties that hold for many of them. Proving this intuition is usually a laborious task, requiring several pages of boring and standard proof. To save this effort, we propose a syntactic ..."
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Cited by 5 (4 self)
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Considering operators defined using Structural Operational Semantics (SOS), commutativity axioms are intuitive properties that hold for many of them. Proving this intuition is usually a laborious task, requiring several pages of boring and standard proof. To save this effort, we propose a syntactic SOS format which guarantees commutativity for a set of composition operators.
The Saga of the Axiomatization of Parallel Composition ⋆
"... Abstract. This paper surveys some classic and recent results on the finite axiomatizability of bisimilarity over CCSlike languages. It focuses, in particular, on nonfinite axiomatizability results stemming from the semantic interplay between parallel composition and nondeterministic choice. The pa ..."
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Cited by 3 (0 self)
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Abstract. This paper surveys some classic and recent results on the finite axiomatizability of bisimilarity over CCSlike languages. It focuses, in particular, on nonfinite axiomatizability results stemming from the semantic interplay between parallel composition and nondeterministic choice. The paper also highlights the role that auxiliary operators, such as Bergstra and Klop’s left and communication merge and Hennessy’s merge operator, play in the search for a finite, equational axiomatization of parallel composition both for classic process algebras and for their realtime extensions. 1 The Problem and its History Process algebras are prototype description languages for reactive systems that arose from the pioneering work of figures like Bergstra, Hoare, Klop and Milner. Wellknown examples of such languages are ACP [18], CCS [44], CSP [40] and Meije [13]. These algebraic description languages for processes differ in the basic collection of operators that they offer for building new process descriptions from existing ones. However, since they are designed to allow for the description and analysis of systems of interacting processes, all these languages contain some form of parallel composition (also known as merge) operator allowing one to put two process terms in parallel with one another. These operators usually interleave the behaviours of their arguments, and support some form of synchronization between them. For example, Milner’s CCS offers the binary operator , whose intended semantics is described by the following classic rules in the style of Plotkin [49]. x µ → x ′ x   y µ → x ′   y y µ → y ′ x   y µ → x   y ′ x α → x ′ , y ¯α → y ′ x   y τ → x ′   y ′ (In the above rules, the symbol µ stands for an action that a process may perform, α and ¯α are two observable actions that may synchronize, and τ is a symbol denoting the result of their synchronization.)
Axiomatizing Weak Ready Simulation Semantics over BCCSP
"... Ready simulation has proven to be one of the most significant semantics in process theory. It is at the heart of a number of general results that pave the way to a comprehensive understanding of the spectrum of process semantics. Since its original definition by Bloom, Istrail and Meyer in 1995, sev ..."
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Cited by 2 (1 self)
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Ready simulation has proven to be one of the most significant semantics in process theory. It is at the heart of a number of general results that pave the way to a comprehensive understanding of the spectrum of process semantics. Since its original definition by Bloom, Istrail and Meyer in 1995, several authors have proposed generalizations of ready simulation to deal with internal actions. However, a thorough study of the (non)existence of finite (in)equational bases for weak ready simulation semantics is still missing in the literature. This paper presents a complete account of positive and negative results on the axiomatizability of weak ready simulation semantics over the language BCCSP. In addition, this study offers a thorough analysis of the axiomatizability properties of weak simulation semantics.
SOS Rule Formats for Zero and Unit Elements
, 2011
"... This paper proposes rule formats for Structural Operational Semantics guaranteeing that certain constants act as left or right unit/zero elements for a set of binary operators. Examples of left and right zero, as well as unit, elements from the literature are shown to fit the rule formats offered in ..."
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Cited by 1 (1 self)
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This paper proposes rule formats for Structural Operational Semantics guaranteeing that certain constants act as left or right unit/zero elements for a set of binary operators. Examples of left and right zero, as well as unit, elements from the literature are shown to fit the rule formats offered in this study.
The equational theory of weak complete simulation semantics over BCCSP
 SOFSEM 2012: Theory and Practice of Computer Science, 38th Conference on Current Trends in Theory and Practice of Computer Science
, 2012
"... Abstract. This paper presents a complete account of positive and negative results on the finite axiomatizability of weak complete simulation semantics over the language BCCSP. We offer finite (un)conditional groundcomplete axiomatizations for the weak complete simulation precongruence. In sharp cont ..."
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Abstract. This paper presents a complete account of positive and negative results on the finite axiomatizability of weak complete simulation semantics over the language BCCSP. We offer finite (un)conditional groundcomplete axiomatizations for the weak complete simulation precongruence. In sharp contrast to this positive result, we prove that, in the presence of at least one observable action, the (in)equational theory of the weak complete simulation precongruence over BCCSP does not have a finite (in)equational basis. In fact, the collection of (in)equations in at most one variable that hold in weak complete simulation semantics over BCCSP does not have an (in)equational basis of ‘bounded depth’, let alone a finite one. 1