Communicating evolving algebras

Glavan, Paola; Rosenzweig, Dean

doi:10.1007/3-540-56992-8_13

Cited by 11 publications

(5 citation statements)

References 6 publications

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“…The results preceding Lemma B.5 are needed for its proof. We start by noticing that the derivation of an interaction can be put into a standard form in which the rule R-EQV is used at most once, at the end (this lemma also appears in Glavan and Rosenzweig (1993).…”

mentioning

confidence: 99%

Typing and subtyping for mobile processes

Pierce¹,

Sangiorgi²

1996

Math. Struct. Comp. Sci.

233

118

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The π-calculus is a process algebra that supports mobility by focusing on the communication of channels. Milner's presentation of the π-calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use. We extend Milner's language of types by distinguishing between the ability to read from a channel, the ability to write to a channel, and the ability both to read and to write. This refinement gives rise to a natural subtype relation similar to those studied in typed λ-calculi. The greater precision of our type discipline yields stronger versions of standard theorems on the π-calculus. These can be used, for example, to obtain the validity of β-reduction for the more efficient of Milner's encodings of the call-by-value λ-calculus, which fails in the ordinary π-calculus. We define the syntax, typing, subtyping, and operational semantics of our calculus, prove that the typing rules are sound, apply the system to Milner's λ-calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing.

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mentioning

confidence: 99%

Typing and subtyping for mobile processes

Pierce¹,

Sangiorgi²

1996

Math. Struct. Comp. Sci.

233

118

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“…Informally, it expresses that after application of the rule r in the given state the location (f, x) (so the length of the tuple x is the arity of f ) will have the value y. In [Glavan and Rosenzweig 1992] and also in [Blass et al 1999] this predicate was written as Update r,f (x, y) to emphasise the extra-logical character of r and f .…”

Section: The Logic Of Non-deterministic Asmsmentioning

confidence: 99%

“…In addition, the usefulness of ASMs for high-level development of complex systems is stressed by Börger in [Börger and Stärk 2003]. Furthermore, logics that enable reasoning about ASMs have been developed for deterministic ASMs by Stärk and Nanchen [Stärk and Nanchen 2001] based on ideas from Glavan and Rosenzweig that had already been exploited for CPT [Glavan and Rosenzweig 1992], and extended to non-deterministic ASMs by Ferrarotti, Schewe, Tec and Wang [Ferrarotti et al 2017;2018], the latter work leading to a fragment of second-order logic with Henkin semantics [Henkin 1950].…”

Section: Introductionmentioning

confidence: 99%

Insignificant Choice Polynomial Time

Schewe

2020

Preprint

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In the late 1980s Gurevich conjectured that there is no logic capturing PTIME, where logic has to be understood in a very general way comprising computation models over structures. In this article we first refute Gurevich's conjecture. For this we extend the seminal research of Blass, Gurevich and Shelah on choiceless polynomial time (CPT), which exploits deterministic Abstract State Machines (ASMs) supporting unbounded parallelism to capture the choiceless fragment of PTIME. CPT is strictly included in PTIME. We observe that choice is unavoidable, but that a restricted version suffices, which guarantees that the final result is independent from the choice. Such a version of polynomially bounded ASMs, which we call insignificant choice polynomial time (ICPT) will indeed capture PTIME. Even more, insignificant choice can be captured by ASMs satisfying a local insignificance condition, which defines a logic capturing PTIME. This condition can be expressed in the logic of non-deterministic ASMs plus inflationary fixed-point. We use this result for our second contribution showing that PTIME differs from NP. For the proof we build again on the research on CPT first establishing a limitation on permutation classes of the sets that can be activated by an ICPT computation. We then prove an equivalence theorem, which characterises structures that cannot be distinguished by the logic. In particular, this implies that SAT cannot be decided by an ICPT computation.

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“…Agents may share functions, and it is convenient [9] to assume that all states of all agents share the same carrier; see the end of 3.2.4 in this connection.…”

Section: Importing Elementsmentioning

confidence: 99%