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...use of so-called fresh nonces to achieve their security assertions [17]. Finally, fresh names are also important in the field of network protocols and are one of the key ingredients of the π-calculus =-=[20]-=-. In general, the equivalence problem of register automata is undecidable (even without freshness). This limits their applicability in active learning, as equivalence queries cannot be implemented (co...

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...utomata based on some partial information, for example samples, which are words that either belong to their accepted language or not. A popular framework is that of active learning defined by Angluin =-=[2]-=- in which a learner may consult a teacher for so-called membership and equivalence queries to eventually infer the automaton in question. Learning automata has a lot of applications in computer scienc...

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...on automaton and increases the number of registers as necessary. Any active learning algorithm for regular languages may be adapted to our setting. Here we describe a variant of Rivest and Schapire’s =-=[22]-=- algorithm which is itself a variant of Angluin’s L ∗ algorithm [2]. An overview of learning algorithms for deterministic finite state automata can be found, for example, in [4]. The algorithm is base...

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...terministic automata, the complexity is polynomial in the number of states and exponential in the number of registers. Applicability of our framework in verification (e.g., compositional verification =-=[10]-=- and infinite state regular model checking [13]) is underpinned by the fact that session automata form a robust language class: While inclusion is undecidable for register automata [21], we show that ...

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...l verification [10] and infinite state regular model checking [13]) is underpinned by the fact that session automata form a robust language class: While inclusion is undecidable for register automata =-=[21]-=-, we show that it is decidable for session automata. In [7], model checking session automata was shown decidable wrt. a powerful monadic second-order logic with data-equality predicate (dMSO). Here, w...

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...ly, data deterministic automata cannot guess if a data value in a register will be reused later. Session automata are expressively incomparable with the various register automata models considered in =-=[16, 21, 23, 9, 14]-=-. In particular, due to freshness, the languages from Ex. 1, 2, and 3 are not recognizable by the models for which a learning algorithm exists [9, 14]. On the other hand, our model cannot recognize “t...

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...alled membership and equivalence queries to eventually infer the automaton in question. Learning automata has a lot of applications in computer science. Notable examples are the use in model checking =-=[12]-=- and testing [3]. See [18] for an overview. While active learning of regular languages is meanwhile well understood and is supported by freely available libraries such as learnlib [19] and libalf [8],...

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...eorem 1. Session automata are strictly more expressive than data deterministic session automata. Session automata are expressively incomparable with the various register automata models considered in =-=[16, 21, 23, 9, 14]-=-. In particular, due to freshness, the languages from Ex. 1, 2, and 3 are not recognizable by the models for which a learning algorithm exists [9, 14]. On the other hand, our model cannot recognize “t...

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...nnot recognize “the set of all data words” or “every two consecutive data values are distinct”. Our automata are subsumed by fresh-register automata [24], class memory automata [5], and data automata =-=[6]-=-. However, no algorithm for the inference of the latter is known. Note that, for ease of presentation, we consider one-dimensional data words, unlike [14] where labels have an arity and can carry seve...

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...ial in the number of states and exponential in the number of registers. Applicability of our framework in verification (e.g., compositional verification [10] and infinite state regular model checking =-=[13]-=-) is underpinned by the fact that session automata form a robust language class: While inclusion is undecidable for register automata [21], we show that it is decidable for session automata. In [7], m...

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...and equivalence queries to eventually infer the automaton in question. Learning automata has a lot of applications in computer science. Notable examples are the use in model checking [12] and testing =-=[3]-=-. See [18] for an overview. While active learning of regular languages is meanwhile well understood and is supported by freely available libraries such as learnlib [19] and libalf [8], extensions beyo...

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...languages are still an area of active research. Recently, automata dealing with potentially infinite data as first class citizens have been studied. Seminal works in this area are that of [1, 15] and =-=[14]-=-. While the first two use abstraction and refinement techniques to cope with infinite data, the second approach learns a sub-class of register automata. In this paper, we follow the work on learning r...

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...ain regular languages are still an area of active research. Recently, automata dealing with potentially infinite data as first class citizens have been studied. Seminal works in this area are that of =-=[1, 15]-=- and [14]. While the first two use abstraction and refinement techniques to cope with infinite data, the second approach learns a sub-class of register automata. In this paper, we follow the work on l...

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...gister automata. However, we study a different model than [14], having the ability to require that input data is fresh in the sense that it has not been seen so far. This feature has been proposed in =-=[24]-=- in the context of semantics of programming languages, as, for ⋆ This work is partially supported by EGIDE/DAAD-Procope (LeMon).hal-00743240, version 3 - 11 Jun 2013 example, fresh names are needed t...

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...[12] and testing [3]. See [18] for an overview. While active learning of regular languages is meanwhile well understood and is supported by freely available libraries such as learnlib [19] and libalf =-=[8]-=-, extensions beyond plain regular languages are still an area of active research. Recently, automata dealing with potentially infinite data as first class citizens have been studied. Seminal works in ...

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...eorem 1. Session automata are strictly more expressive than data deterministic session automata. Session automata are expressively incomparable with the various register automata models considered in =-=[16, 21, 23, 9, 14]-=-. In particular, due to freshness, the languages from Ex. 1, 2, and 3 are not recognizable by the models for which a learning algorithm exists [9, 14]. On the other hand, our model cannot recognize “t...

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...el session automata. They are well-suited whenever fresh values are important for a finite period, for which they will be stored in one of the registers. Session automata correspond to the model from =-=[7]-=- without stacks. They are incomparable with the model from [14]. Session automata accept data words, i.e., words over an alphabet Σ × D, where Σ is a finite set of labels and D an infinite set of data...

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... = dj. For more background on dMSO, we refer the reader to the appendix and [21, 23, 6]. Note that dMSO is a very expressive logic and goes beyond virtually all automata models defined for data words =-=[21, 6, 11]-=-. We identify a fragment of dMSO, called session MSO logic, that is expressively equivalent to session automata. While register automata also enjoy a logical characterization [11], we are not aware of...

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...alence queries to eventually infer the automaton in question. Learning automata has a lot of applications in computer science. Notable examples are the use in model checking [12] and testing [3]. See =-=[18]-=- for an overview. While active learning of regular languages is meanwhile well understood and is supported by freely available libraries such as learnlib [19] and libalf [8], extensions beyond plain r...

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...eorem 1. Session automata are strictly more expressive than data deterministic session automata. Session automata are expressively incomparable with the various register automata models considered in =-=[16, 21, 23, 9, 14]-=-. In particular, due to freshness, the languages from Ex. 1, 2, and 3 are not recognizable by the models for which a learning algorithm exists [9, 14]. On the other hand, our model cannot recognize “t...

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... model checking [12] and testing [3]. See [18] for an overview. While active learning of regular languages is meanwhile well understood and is supported by freely available libraries such as learnlib =-=[19]-=- and libalf [8], extensions beyond plain regular languages are still an area of active research. Recently, automata dealing with potentially infinite data as first class citizens have been studied. Se...

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...ther hand, our model cannot recognize “the set of all data words” or “every two consecutive data values are distinct”. Our automata are subsumed by fresh-register automata [24], class memory automata =-=[5]-=-, and data automata [6]. However, no algorithm for the inference of the latter is known. Note that, for ease of presentation, we consider one-dimensional data words, unlike [14] where labels have an a...

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... in object-oriented languages. Moreover, fresh data values are important ingredients in modeling security protocols which often make use of so-called fresh nonces to achieve their security assertions =-=[17]-=-. Finally, fresh names are also important in the field of network protocols and are one of the key ingredients of the π-calculus [20]. In general, the equivalence problem of register automata is undec...

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...Rivest and Schapire’s [22] algorithm which is itself a variant of Angluin’s L ∗ algorithm [2]. An overview of learning algorithms for deterministic finite state automata can be found, for example, in =-=[4]-=-. The algorithm is based on the notion of observation table which contains the information accumulated by the learner during the learning process. An observation table over a given alphabet Σ × Γk is ...