Symbolic Semantics Research Articles

Symbolic and Asynchronous Semantics via Normalized Coalgebras

The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons infinite, symbolic semantics were introduced as a mean to define smaller, possibly finite, transition systems, by employing symbolic actions and avoiding some sources of infiniteness. Unfortunately, symbolic bisimilarity has a different shape with respect to ordinary bisimilarity, and thus the standard coalgebraic characterization does not work. In this paper, we introduce its coalgebraic models. We will use as motivating examples two asynchronous formalisms: open Petri nets and asynchronous pi-calculus. Indeed, as we have shown in a previous paper, asynchronous bisimilarity can be seen as an instance of symbolic bisimilarity.

Symbolic bisimulation for the applied pi calculus*

We propose a symbolic semantics for the finite applied pi calculus. The applied pi calculus is a variant of the pi calculus with extensions for modelling cryptographic protocols. By treating inputs symbolically, our semantics avoids potentially infin

A process calculus for Mobile Ad Hoc Networks

We present the ω -calculus, a process calculus for formally modeling and reasoning about Mobile Ad Hoc Wireless Networks (MANETs) and their protocols. The ω -calculus naturally captures essential characteristics of MANETs, including the ability of a MANET node to broadcast a message to any other node within its physical transmission range (and no others), and to move in and out of the transmission range of other nodes in the network. A key feature of the ω -calculus is the separation of a node’s communication and computational behavior, described by an ω -process, from the description of its physical transmission range, referred to as an ω -process interface. Our main technical results are as follows. We give a formal operational semantics of the ω -calculus in terms of labeled transition systems and show that the state reachability problem is decidable for finite-control ω -processes. We also prove that the ω -calculus is a conservative extension of the π -calculus, and that late bisimulation equivalence (appropriately lifted from the π -calculus to the ω -calculus) is a congruence. Congruence results are also established for a weak version of late bisimulation equivalence, which abstracts away from two types of internal actions: τ -actions, as in the π -calculus, and μ -actions, signaling node movement. We additionally define a symbolic semantics for the ω -calculus extended with the mismatch operator, along with a corresponding notion of symbolic bisimulation equivalence, and establish congruence results for this extension as well. Finally, we illustrate the practical utility of the calculus by developing and analyzing formal models of a leader election protocol for MANETs and the AODV routing protocol.

On Symbolic Semantics for Name-decorated Contexts

Under several regards, various of the recently proposed computational paradigms are open-ended, i.e. they may comprise components whose behaviour is not or cannot be fully specified. For instance, applications can be distributed across different administration domains that do not fully disclose their internal business processes to each other, or the dynamics of the system may allow reconfigurations and dynamic bindings whose specification is not available at design time. While a large set of mature design and analysis techniques for closed systems have been developed, their lifting to the open case is not always straightforward. Some existing approaches in the process calculi community are based on the need of proving properties for components that may hold in any, or significantly many, execution environments. Dually, frameworks describing the dynamics of systems with unspecified components have also been presented. In this paper we lay some preliminary ideas on how to extend a symbolic semantics model for open systems in order to deal with name-based calculi. Moreover, we also discuss how the use of a simple type system based on name-decoration for unknown components can improve the expressiveness of the framework. The approach is illustrated on a simple, paradigmatic calculus of web crawlers, which can be understood as a term representation of a simple class of graphs.

A Symbolic Semantics for a Calculus for Service-Oriented Computing

We introduce a symbolic characterisation of the operational semantics of COWS, a formal language for specifying and combining service-oriented applications, while modelling their dynamic behaviour. This alternative semantics avoids infinite representations of COWS terms due to the value-passing nature of communication in COWS and is more amenable for automatic manipulation by analytical tools, such as e.g. equivalence and model checkers. We illustrate our approach through a ‘translation service’ scenario.

Logic of proofs with substitution

The substitution operation in logic of proofs is axiomatized. For the system constructed, symbolic semantics is introduced and a completeness theorem is proved.

A semantic framework for open processes

We propose a general methodology for analysing the behaviour of open systems modelled as coordinators, i.e., open terms of suitable process calculi. A coordinator is understood as a process with holes or placeholders where other coordinators and components (i.e., closed terms) can be plugged in, thus influencing its behaviour. The operational semantics of coordinators is given by means of a symbolic transition system, where states are coordinators and transitions are labeled by spatial/modal formulae expressing the potential interaction that plugged components may enable. Behavioural equivalences for coordinators, like strong and weak bisimilarities, can be straightforwardly defined over such a transition system. Different from other approaches based on universal closures, i.e., where two coordinators are considered equivalent when all their closed instances are equivalent, our semantics preserves the openness of the system during its evolution, thus allowing dynamic instantiation to be accounted for in the semantics. To further support the adequacy of the construction, we show that our symbolic equivalences provide correct approximations of their universally closed counterparts, coinciding with them over closed components. For process calculi in suitable formats, we show how tractable symbolic semantics can be defined constructively using unification.

Two Case Studies of Semantics Execution in Maude: CCS and LOTOS

We explore the features of rewriting logic and, in particular, of the rewriting logic language Maude as a logical and semantic framework for representing and executing inference systems. In order to illustrate the general ideas we consider two substantial case studies. In the first one, we represent both the semantics of Milner's CCS and a modal logic for describing local capabilities of CCS processes. Although a rewriting logic representation of the CCS semantics is already known, it cannot be directly executed in the default interpreter of Maude. Moreover, it cannot be used to answer questions such as which are the successors of a process after performing an action, which is used to define the semantics of Hennessy-Milner modal logic. Basically, the problems are the existence of new variables in the righthand side of the rewrite rules and the nondeterministic application of the semantic rules, inherent to CCS. We show how these problems can be solved in a general, not CCS dependent way by controlling the rewriting process by means of reflection. This executable specification plus the reflective control of rewriting can be used to analyze CCS processes. The same techniques are also used to implement a symbolic semantics for LOTOS in our second case study. The good properties of Maude as a metalanguage allow us to implement a whole formal tool where LOTOS specifications without restrictions in their data types (given as ACT ONE specifications) can be executed. In summary, we present Maude as an executable semantic framework by providing easy-tool-building techniques for a language given its operational semantics.

Negative Operations on Proofs and Labels

Logic of proofs ℒ𝒫 introduced by S. Artemov in 1995 describes properties of proof predicate ‘t is a proof of F’ in the propositional language extended by atoms of the form [[t]]F. Proof are represented by terms constructed by three elementary recursive operations on proofs. In order to make the language more expressive we introduce the additional storage predicate with the intended interpretation ‘x is a label for F’. It can play the role of syntax encoding, so it is useful for specification of operations that require formula arguments. In this paper we study operations on proofs and labels that can be specified in the extended language. First, we give a formal definition of an operation on proofs and labels. Then, for an arbitrary finite set of operations ℱ the logic ℒ𝒫𝒮(ℱ) is defined. We provide ℒ𝒫𝒮(ℱ) with symbolic semantics and arithmetical semantics. The main result of the paper is the uniform completeness theorem for this family of logics with respect to the both types of semantics.

Efficient Guiding Towards Cost-Optimality in UPPAAL

<p>In this paper we present an algorithm for efficiently computing<br /> the minimum cost of reaching a goal state in the model of Uniformly<br />Priced Timed Automata (UPTA). This model can be seen as a submodel<br />of the recently suggested model of linearly priced timed automata, which<br />extends timed automata with prices on both locations and transitions.<br />The presented algorithm is based on a symbolic semantics of UTPA, and<br />an efficient representation and operations based on difference bound <br />matrices. In analogy with Dijkstra's shortest path algorithm, we show that<br />the search order of the algorithm can be chosen such that the number of<br />symbolic states explored by the algorithm is optimal, in the sense that<br />the number of explored states can not be reduced by any other search<br />order based on the cost of states. We also present a number of techniques<br />inspired by branch-and-bound algorithms which can be used for limiting<br />the search space and for quickly finding near-optimal solutions.<br />The algorithm has been implemented in the verification tool Uppaal.<br />When applied on a number of experiments the presented techniques <br />reduced the explored state-space with up to 90%.</p>

A symbolic semantics for abstract model checking

In this paper we present a symbolic semantics of value-passing concurrent processes where classical branching is replaced by separate relations of non-deterministic branch and alternative choice. The obtained symbolic graph is finite for regular processes and can suitably be interpreted over abstract values to effectively compute a safe abstract model for full μ-calculus model checking. The representation of non-determinism and alternative choice in symbolic transitions allows to achieve more precise approximations of the two dual next modalities.

Time and Eternity in the Eschatology of the Guennol Triptych

"Time and Eternity in the Eschatology of the Guennol Triptych," The paper investigates the symbolic and scholastic semantics underlying a distinct group of enamel triptychs originating in the Mosan-Rhenish region between 1160 and 1175, concentrating on the so-called Guennol triptych, conserved at the cloisters, It represents the Last Judgment in a very unusual way, without judge, without court, without terror, but with a splinter of the holy cross as the sign of the Son of man, thus actualizing the imminence of the Last Judgment. The texts exactly describing the elements of this astonishing setting are identified as distinctions 45-49 of the fourth book of Lombard's Sentences.

A modal logic for message passing processes

A first-order modal logic is given for describing properties of processes which may send and receive values or messages along communication ports. We give two methods for proving that a process enjoys such a property. The first is the construction, for each process P and formula F, of a characteristic formula P sat F such that P enjoys the property F if and only if the formula P sat F is logically equivalent to tt. The second is a sound and complete proof system whose judgements take the form B ⊢ P∶F, meaning: under the assumption B the process P enjoys the property F. The notion of symbolic operational semantics plays a crucial role in the design of both the characteristic formulae and the proof system.

Software development

We propose a language-independent symbolic execution framework for languages endowed with a formal operational semantics based on term rewriting. Starting from a given definition of a language, a new language definition is generated, with the same syntax as the original one, but whose semantical rules are transformed in order to rewrite over logical formulas denoting possibly infinite sets of program states. Then, the symbolic execution of concrete programs is, by definition, the execution of the same programs with the symbolic semantics. We prove that the symbolic execution thus defined has the properties naturally expected from it (with respect to concrete program execution). A prototype implementation of our approach was developed in the K framework. We demonstrate the tool׳s genericity by instantiating it on several languages, and illustrate it on the reachability analysis and model checking of several programs.

Symbolic Semantics and Program Reduction

A class of transformations of functional programs based on symbolic execution and simplification of conditionals is presented. The operational symbolic semantics of a family of functional languages is defined exploiting a set-theoretic notion of symbolic constants. An effective transformation able to simplify a functional program via removal of conditionals is discussed. Finally, it is shown that a structural approach, based on abstract data type specifications, provides a suitable representation for symbolic constants.

Symbolic and Pragmatic Semantics: A Kannada System of Address

Symbolic and Pragmatic Semantics: A Kannada System of Address

Seldom is heard a discouraging word in Kannada address

Susan S. Bean. Symbolic and Pragmatic Semantics; A Kannada System of Address. Chicago and London: Chicago University Press, 1978. xvi +163 pp. Tables, figures, appendices, notes, bibliography and index. $17.00.

Book Review: IV. Pastoral — Practical Studies: The Art of Awareness, Language as Symbolic Action, Semantics and Common Sense, Preparing for Platform and Pulpit

Book Review: IV. Pastoral — Practical Studies: The Art of Awareness, Language as Symbolic Action, Semantics and Common Sense, Preparing for Platform and Pulpit