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The execution of sequential programs allows them to be represented using mathematical functions formed by the composition of statements following one after the other. Each such statement is in itself a partial function, which allows only inputs satisfying a particular Boolean condition to carry forward the execution and hence, the composition of such functions (as a result of sequential execution of the statements) strengthens the valid set of input state variables for the program to complete its execution and halt succesfully. With this thought in mind, this paper tries to study a particular class of partial functions, which tend to preserve the truth of two given Boolean conditions whenever the state variables satisfying one are mapped through such functions into a domain of state variables satisfying the other. The existence of such maps allows us to study isomorphism between different programs, based not only on their structural characteristics (e.g. the kind of programming constructs used and the overall input-output transformation), but also the nature of computation performed on seemingly different inputs. Consequently, we can now relate programs which perform a given type of computation, like a loop counting down indefinitely, without caring about the input sets they work on individually or the set of statements each program contains.
This paper investigates the usage of generating functions (GFs) encoding measures over the program variables for reasoning about discrete probabilistic programs. To that end, we define a denotational GF-transformer semantics for probabilistic while-p
The current work introduces the notion of pdominant sets and studies their recursion-theoretic properties. Here a set A is called pdominant iff there is a partial A-recursive function {psi} such that for every partial recursive function {phi} and alm
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursi
This paper poses that transition systems constitute a good model of distributed systems only in combination with a criterion telling which paths model complete runs of the represented systems. Among such criteria, progress is too weak to capture rele
The classical sequential growth model for causal sets provides a template for the dynamics in the deep quantum regime. This growth dynamics is intrinsically temporal and causal, with each new element being added to the existing causal set without dis