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62
Relational Reasoning about Functions and Nondeterminism
, 1998
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Dissertation Series publications. Copies may be obtained by contacting: BRICS ..."
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Cited by 31 (4 self)
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Dissertation Series publications. Copies may be obtained by contacting: BRICS
Effective Transformations on Infinite Trees, with Applications to High Undecidability, Dominoes, and Fairness
 Journal of the ACM
, 1986
"... Elementary translations between various kinds of recursive trees arc prcsented. It is shown that trees of either finite. or countably infinite branching can be effectively put into oneone correspondence with infinitely branching trees in such a way that the infinite paths of the latter correspond t ..."
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Cited by 26 (3 self)
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Elementary translations between various kinds of recursive trees arc prcsented. It is shown that trees of either finite. or countably infinite branching can be effectively put into oneone correspondence with infinitely branching trees in such a way that the infinite paths of the latter correspond to the Vabiding infinite paths of the former. Here V can be any member of a very wide class of properties of infinite paths. For many properties P, the converse holds too. Two of the applications involve (a) the formulation of large classes of highly undecidable variants of classical computational problems, and in particular, easily describable domino problems that are Illcomplete, and (b) the existence of a general method for proving termination of nondeterministic or concurrent programs under any reasonable notion of fairness.
Hoare Logics for Recursive Procedures and Unbounded Nondeterminism
 COMPUTER SCIENCE LOGIC (CSL 2002), VOLUME 2471 OF LNCS
, 2002
"... This paper presents sound and complete Hoare logics for partial and total correctness of recursive parameterless procedures in the context of unbounded nondeterminism. For total correctness, the literature so far has either restricted recursive procedures to be deterministic or has studied unbounde ..."
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Cited by 26 (3 self)
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This paper presents sound and complete Hoare logics for partial and total correctness of recursive parameterless procedures in the context of unbounded nondeterminism. For total correctness, the literature so far has either restricted recursive procedures to be deterministic or has studied unbounded nondeterminism only in conjunction with loops rather than procedures. We consider both single procedures and systems of mutually recursive procedures. All proofs have been checked with the theorem prover Isabelle/HOL.
Polynomial Constants are Decidable
 In 9th Static Analysis Symposium (SAS
, 2002
"... Abstract. Constant propagation aims at identifying expressions that always yield a unique constant value at runtime. It is wellknown that constant propagation is undecidable for programs working on integers even if guards are ignored as in nondeterministic flow graphs. We show that polynomial con ..."
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Cited by 24 (6 self)
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Abstract. Constant propagation aims at identifying expressions that always yield a unique constant value at runtime. It is wellknown that constant propagation is undecidable for programs working on integers even if guards are ignored as in nondeterministic flow graphs. We show that polynomial constants are decidable in nondeterministic flow graphs. In polynomial constant propagation, assignment statements that use the operators +, −, ∗ are interpreted exactly but all assignments that use other operators are conservatively interpreted as nondeterministic assignments. We present a generic algorithm for constant propagation via a symbolic weakest precondition computation and show how this generic algorithm can be instantiated for polynomial constant propagation by exploiting techniques from computable ring theory. 1
Uncountable Limits and the Lambda Calculus
, 1995
"... . In this paper we address the problem of solving recursive domain equations using uncountable limits of domains. These arise for instance, when dealing with the ! 1 continuous functionspace constructor and are used in the denotational semantics of programming languages which feature unbounded cho ..."
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Cited by 22 (1 self)
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. In this paper we address the problem of solving recursive domain equations using uncountable limits of domains. These arise for instance, when dealing with the ! 1 continuous functionspace constructor and are used in the denotational semantics of programming languages which feature unbounded choice constructs. Surprisingly, the category of cpo's and ! 1 continuous embeddings is not ! 0 cocomplete. Hence the standard technique for solving reflexive domain equations fails. We give two alternative methods. We discuss also the issue of completeness of the fijcalculus w.r.t reflexive domain models. We show that among the reflexive domain models in the category of cpo's and ! 0 continuous functions there is one which has a minimal theory. We give a reflexive domain model in the category of cpo's and ! 1 continuous functions whose theory is precisely the fij theory. So ! 1 continuous models are complete for the fijcalculus. CR Classification: F.3.2, F.4.1, D.3.3 Key words: count...
Expressiveness Results for Process Algebras
, 1993
"... The expressive power of process algebras is investigated in a general setting of structural operational semantics. The notion of an effective operational semantics is introduced and it is observed that no effective operational semantics for an enumerable language can specify all effective process ..."
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Cited by 21 (2 self)
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The expressive power of process algebras is investigated in a general setting of structural operational semantics. The notion of an effective operational semantics is introduced and it is observed that no effective operational semantics for an enumerable language can specify all effective process graphs up to trace equivalence. A natural class of Plotkin style SOS specifications is identified, containing the guarded versions of calculi like CCS, SCCS, Meije and ACP, and it is proved that any specification in this class induces an effective operational semantics. Using techniques introduced by Bloom, it is shown that for the guarded versions of CCSlike calculi, there is a double exponential bound on the speed with which the number of outgoing transitions in a state can grow. As a corollary of this result it follows that two expressiveness results of De Simone for Meije and SCCS depend in a fundamental way on the use of unguarded recursion. A final result of this paper is that all operators definable via a finite number of rules in a format due to De Simone, are derived operators in the simple process calculus PC. 1991 Mathematics Subject Classification: 68Q05, 68Q10, 68Q55, 68Q75, 03D20. 1991 CR Categories: D.3.1, D.3.3, F.1.1, F.1.2, F.3.2, F.4.1. Keywords & Phrases: process algebra, PC, labeled transition systems, process graphs, effective process graphs, effective operational semantics, structural operational semantics, expressiveness, bisimulation equivalence, trace equivalence, action transducers. Notes: Most of this work was carried out while the author was at the MIT Laboratory for Computer Science, supported by ONR contract N0001485K0168. Part of this work took place in the context of the ESPRIT Basic Research Action 7166, CONCUR2. This p...
Computations, residuals and the power of indeterminacy
 In Timo Lepisto and Arto Salomaa, editors, Proceedings of the Fifteenth ICALP
, 1988
"... We investigate the power of Katmstyle datattow networks, with processes that may exhibit indeterminate behavior. Our main result is a theorem about networks of "monotone " processes, which shows: (1) that the input/output relation of such a network is a total and monotone relation; and (2) every re ..."
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Cited by 20 (10 self)
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We investigate the power of Katmstyle datattow networks, with processes that may exhibit indeterminate behavior. Our main result is a theorem about networks of "monotone " processes, which shows: (1) that the input/output relation of such a network is a total and monotone relation; and (2) every relation that is total, monotone, and continuous in a certain sense, is the input/output relation of such a network. Now, the class of monotone networks includes networks that compute arbitrary continuous inpu*~/output functions, an "angelic merge " network, and an "ilffinityfair merge " network that exhibits countably indeterminate branching. Since the "fair merge " relation is neither monotone nor continuous, a corollary of our main result is the impossibility of implementing fair merge in terms of continuous functions, angelic merge, and infinityfair merge. Our results are established by applying the powerftll technique of "residuals " to the computations of a network. Residuals, which have previously been used to investigate optimal reduction strategies for the Acalculus, have recently been demonstrated by one of the authors (Stark) "also to be of use in reasoning about concurrent systems. Here, we define the general notion of a "residual operation " on an automaton, and show how residual operations defined on the components of a network induce a certain preorder E on the set of computations of the network. For networks of "monotone port automata, " we show that the "fair " computations coincide with Xmaximal computations. Our results follow from this extremely convenient property. 1
The expressive power of indeterminate dataflow primitives
 Information and Computation
, 1992
"... We analyze the relative expressive power of variants of the indeterminate fair merge operator in the context of static dataflow. We establish that there are three different, provably inequivalent, forms of unbounded indeterminacy. In particular, we show that the wellknown fair merge primitive canno ..."
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Cited by 17 (7 self)
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We analyze the relative expressive power of variants of the indeterminate fair merge operator in the context of static dataflow. We establish that there are three different, provably inequivalent, forms of unbounded indeterminacy. In particular, we show that the wellknown fair merge primitive cannot be expressed with just unbounded indeterminacy. Our proofs are based on a simple trace semantics and on identifying properties of the behaviors of networks that are invariant under network composition. The properties we consider in this paper are all generalizations of monotonicity. 1
Separation logic for higherorder store
 Pages 575–590 of: Computer Science Logic. Lecture Notes in Computer Science
, 2006
"... Abstract. Separation Logic is a substructural logic that supports local reasoning for imperative programs. It is designed to elegantly describe sharing and aliasing properties of heap structures, thus facilitating the verification of programs with pointers. In past work, separation logic has been d ..."
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Cited by 16 (3 self)
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Abstract. Separation Logic is a substructural logic that supports local reasoning for imperative programs. It is designed to elegantly describe sharing and aliasing properties of heap structures, thus facilitating the verification of programs with pointers. In past work, separation logic has been developed for heaps containing records of basic data types. Languages like C or ML, however, also permit the use of code pointers. The corresponding heap model is commonly referred to as “higherorder store ” since heaps may contain commands which in turn are interpreted as partial functions between heaps. In this paper we make Separation Logic and the benefits of local reasoning available to languages with higherorder store. In particular, we introduce an extension of the logic and prove it sound, including the Frame Rule that enables specifications of code to be extended by invariants on parts of the heap that are not accessed. 1