Stimulus Equivalence: A Comparison of Operant and Associative Procedures

Previous studies comparing the effectiveness of the stimulus-pairing-observation and matching-to-sample procedures in facilitating the formation of equivalence relations have had conflicting findings. In an attempt to clarify the reasons for this, Experiment 1 replicated one of the experiments from Leader and Barnes-Holmes (2001b) but with the Chinese characters used by Clayton and Hayes (2004) as stimuli. The adult participants completed both the stimulus-pairing-observation and matching-to-sample procedures. Neither procedure was found to be more effective than the other, with few of the participants demonstrating equivalence after either procedure. Due to the failure of most participants to demonstrate equivalence, Experiment 2 replicated Experiment 1 but with the original nonsense syllables used by Leader and Barnes-Holmes (2001b). Equivalence was not demonstrated by any of the participants in Experiment 2. Therefore, the failures in Experiment 1 were not the result of the stimuli used. The use of the same stimuli in conflicting relations was identified as the most likely cause. Experiment 3 addressed this by using different nonsense syllables with each procedure. This resulted in greater accuracy on both the symmetry and equivalence tests compared to the earlier experiments; however, none of the participants demonstrated equivalence, and the procedures did not differ in their effectiveness. In Experiments 4 to 6 participants experienced either the stimulus-pairing observation or matching-to-sample procedures. These three experiments examined the effect of instructional specificity, stimulus arrangement, and the number of training trials on the effectiveness of these two procedures. Experiment 4 found that instructions which outlined the task required more specifically increase the effectiveness of both procedures marginally, and that a larger number of training and testing cycles (compared to e 1-3) did not aid in the development of equivalence. Experiment 5 examined the effectiveness of the many-to-one or one-to-many stimulus arrangements (compared to the linear arrangement used in the earlier experiments). The many-to-one and one-to-many arrangements resulted in more participants demonstrating equivalence than the linear arrangement for both the stimulus-pairing-observation and matching-to-sample procedures. Experiment 6 replicated E 5 but with more training trials prior to each equivalence test. This resulted in more participants demonstrating equivalence across both procedures and all stimulus arrangements. The stimulus-pairing-observation and matching-to-sample procedures were found to be equally effective in terms of accuracy achieved on the equivalence tests; however, the matching-to-sample procedure resulted in the development of equivalence within fewer training trials than the stimulus-pairing-observation procedure. When the stimulus-pairing-observation procedure was used, more participants demonstrated equivalence with the one-to-many arrangement than with the many-to-one or linear arrangements. When the matching-to-sample procedure was used, the one-to-many and many-to-one arrangements resulted in more participants demonstrating equivalence than the linear arrangement. Comparisons across the experiments suggested that the number of training trials completed prior to each equivalence test, but not the total number of training trials completed, affected performance. The effectiveness of the stimulus arrangements differed across the procedures, but one-to-many arrangement was more effective than the linear arrangement for both procedures. Overall, these experiments suggest that there is little difference in the effectiveness of the MTS and SPO procedures in facilitating the formation of equivalence relations, and that the development of equivalence is made more likely for both procedures by the addition of more training trials prior to each test, and the use of a one-to-many stimulus arrangement

Structural Rewriting in the pi-Calculus

We consider reduction in the synchronous pi-calculus with replication, without sums. Usual definitions of reduction in the pi-calculus use a closure w.r.t. structural congruence of processes. In this paper we operationalize structural congruence by providing a reduction relation for pi-processes which also performs necessary structural conversions explicitly by rewrite rules. As we show, a subset of structural congruence axioms is sufficient. We show that our rewrite strategy is equivalent to the usual strategy including structural congruence w.r.t.the observation of barbs and thus w.r.t. may- and should-testing equivalence in the pi-calculus

Stochastic systems divergence through reinforcement learning

Les mathématiques offrent un cadre convenable pour raisonner rigoureusement sur les systèmes et phénomènes réels. Par exemple, en génie logiciel, les méthodes formelles sont parmi les outils les plus efficaces pour détecter les anomalies dans les logiciels. Plusieurs systèmes réels sont stochastiques par nature dans le sens où leur comportement est sujet à un aspect d'incertitude. La représentation de ce genre de systèmes requiert des modèles stochastiques comme les processus de Markov étiquetés (LMP), les processus de Markov décisionnels (MDP), etc. Cette thèse porte sur la quantification de la différence entre les systèmes stochastiques. Les contributions majeures sont : 1. une nouvelle approche pour quantifier la divergence entre les systèmes stochastiques basée sur l'apprentissage par renforcement, 2. une nouvelle famille de notions d'équivalence qui se situe entre l'équivalence par trace et la bisimulation, et 3. un cadre plus flexible pour la définition des notions d'équivalence qui se base sur les tests. Le résultat principal de la thèse est que l'apprentissage par renforcement, qui est une branche de l'intelligence artificielle particulièrement efficace en présence d'incertitude, peut être utilisé pour quantifier efficacement cette divergence. L'idée clé est de définir un MDP à partir des systèmes à comparer de telle sorte que la valeur optimale de cet MDP corresponde à la divergence entre eux. La caractéristique la plus attrayante de l'approche proposée est qu'elle est complètement indépendante des structures internes des systèmes à comparer. Pour cette raison, l'approche peut être appliquée à différents types de systèmes stochastiques. La deuxième contribution est une nouvelle famille de notions d'équivalence, que nous appelons moment, qui est plus forte que l'équivalence par trace mais plus faible que la bisimulation. Cette famille se définit naturellement à travers la coïncidence de moments de variable aléatoires (d'où son nom) et possède une caractérisation simple en terme de tests. Nous montrons que moment fait partie d'un cadre plus grand, appelé test-observation-equivalence (TOE), qui constitue la troisième contribution de cette thèse. Il s'agit d'un cadre plus flexible pour la définition des notions d'équivalence basé sur les tests.Modelling real-life systems and phenomena using mathematical based formalisms is ubiquitous in science and engineering. The reason is that mathematics offer a suitable framework to carry out formal and rigorous analysis of these systems. For instance, in software engineering, formal methods are among the most efficient tools to identify flaws in software. The behavior of many real-life systems is inherently stochastic which requires stochastic models such as labelled Markov processes (LMPs), Markov decision processes (MDPs), predictive state representations (PSRs), etc. This thesis is about quantifying the difference between stochastic systems. The main contributions are: 1. a new approach to quantify the divergence between pairs of stochastic systems based on reinforcement learning, 2. a new family of equivalence notions which lies between trace equivalence and bisimulation, and 3. a refined testing framework to define equivalence notions. The important point of the thesis is that reinforcement learning (RL), a branch of artificial intelligence particularly efficient in presence of uncertainty, can be used to quantify efficiently the divergence between stochastic systems. The key idea is to define an MDP out of the systems to be compared and then to interpret the optimal value of the MDP as the divergence between them. The most appealing feature of the proposed approach is that it does not rely on the knowledge of the internal structure of the systems. Only a possibility of interacting with them is required. Because of this, the approach can be extended to different types of stochastic systems. The second contribution is a new family of equivalence notions, moment, that constitute a good compromise between trace equivalence (too weak) and bisimulation (too strong). This family has a natural definition using coincidence of moments of random variables but more importantly, it has a simple testing characterization. moment turns out to be part of a bigger framework called test-observation-equivalence (TOE), which we propose as a third contribution of this thesis. It is a refined testing framework to define equivalence notions with more flexibility

Behavioral Equivalences

Beahvioral equivalences serve to establish in which cases two reactive (possible concurrent) systems offer similar interaction capabilities relatively to other systems representing their operating environment. Behavioral equivalences have been mainly developed in the context of process algebras, mathematically rigorous languages that have been used for describing and verifying properties of concurrent communicating systems. By relying on the so called structural operational semantics (SOS), labelled transition systems, are associated to each term of a process algebra. Behavioral equivalences are used to abstract from unwanted details and identify those labelled transition systems that react “similarly” to external experiments. Due to the large number of properties which may be relevant in the analysis of concurrent systems, many different theories of equivalences have been proposed in the literature. The main contenders consider those systems equivalent that (i) perform the same sequences of actions, or (ii) perform the same sequences of actions and after each sequence are ready to accept the same sets of actions, or (iii) perform the same sequences of actions and after each sequence exhibit, recursively, the same behavior. This approach leads to many different equivalences that preserve significantly different properties of systems

Conflicts and projections

This paper studies abstraction methods suitable to verify very large models of discrete-event systems to be nonconflicting. It compares the observer property to methods known from process algebra, namely to conflict equivalence and observation equivalence. The observer property is shown to be the property that corresponds to conflict equivalence in the case where natural projection is used for abstraction. In this case, the observer property turns out to be the least restrictive condition that can be imposed on natural projection to enable compositional reasoning about conflicts. The observer property is also shown to be closely related to observation equivalence. Several examples and propositions are presented to relate different aspects of these methods of abstraction

A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences

Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models

Modular nonblocking verification using conflict equivalence

This paper proposes a modular approach to verifying whether a large discrete event system is nonconflicting. The new approach avoids computing the synchronous product of a large set of finite-state machines. Instead, the synchronous product is computed gradually, and intermediate results are simplified using conflict-preserving abstractions based on process-algebraic results about fair testing. Heuristics are used to choose between different possible abstractions. Experimental results show that the method is applicable to finite-state machine models of industrial scale and brings considerable improvements in performance over other methods