What is a basic automata-theoretic model of computation with names and fresh-name generation? We introduce Fresh-Register Automata (FRA), a new class of automata which operate on an infinite alphabet of names and use a finite number of registers to store fresh names, and to compare incoming names with previously stored ones. These finite machines extend Kaminski and Francez's Finite-Memory Automata by being able to recognise globally fresh inputs, that is, names fresh in the whole current run. We examine the expressivity of FRA's both from the aspect of accepted languages and of bisimulation equivalence. We establish primary properties and connections between automata of this kind, and answer key decidability questions. As a demonstrating example, we express the theory of the pi-calculus in FRA's and characterise bisimulation equivalence by an appropriate, and decidable in the finitary case, notion in these automata.

Category theory can be seen as a "generalised theory of functions", where the focus is shifted from the pointwise, set-theoretic view of functions, to an abstract view of functions as arrows.Let us briefly recall the arrow notation for functions between sets. 1 A function f with domain X and codomain Y is denoted by: f : X → Y .

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We present a full classification of decidable and undecidable cases for contextual equivalence in a finitary ML-like language equipped with full ground storage (both integers and reference names can be stored). The simplest undecidable type is unit → unit → unit. At the technical level, our results marry game semantics with automata-theoretic techniques developed to handle infinite alphabets. On the automata-theoretic front, we show decidability of the emptiness problem for register pushdown automata extended with fresh-symbol generation.

We propose TOPL automata as a new method for runtime verification of systems with unbounded resource generation. Paradigmatic such systems are object-oriented programs which can dynamically generate an unbounded number of fresh object identities during their execution. Our formalism is based on register automata, a particularly successful approach in automata over infinite alphabets which administers a finite-state machine with boundedly many inputstoring registers. We show that TOPL automata are equally expressive to register automata and yet suitable to express properties of programs. Compared to other runtime verification methods, our technique can handle a class of properties beyond the reach of current tools. We show in particular that properties which require value updates are not expressible with current techniques yet are naturally captured by TOPL machines. On the practical side, we present a tool for runtime verification of Java programs via TOPL properties, where the trade-off between the coverage and the overhead of the monitoring system is tunable by means of a number of parameters. We validate our technique by checking properties involving multiple objects and chaining of values on large open source projects.