Specification Format for Reactive Synthesis Problems

Automatic synthesis from a given specification automatically constructs correct implementation. This frees the user from the mundane implementation work, but still requires the specification. But is specifying easier than implementing? In this paper, we propose a user-friendly format to ease the specification work, in particularly, that of specifying partial implementations. Also, we provide scripts to convert specifications in the new format into the SYNTCOMP format, thus benefiting from state of the art synthesizers.Comment: In Proceedings SYNT 2015, arXiv:1602.0078

Parameterized Synthesis Case Study: AMBA AHB (extended version)

We revisit the AMBA AHB case study that has been used as a benchmark for several reactive syn- thesis tools. Synthesizing AMBA AHB implementations that can serve a large number of masters is still a difficult problem. We demonstrate how to use parameterized synthesis in token rings to obtain an implementation for a component that serves a single master, and can be arranged in a ring of arbitrarily many components. We describe new tricks -- property decompositional synthesis, and direct encoding of simple GR(1) -- that together with previously described optimizations allowed us to synthesize the model with 14 states in 30 minutes.Comment: Moved to appendix some not very important proofs. To section 'optimizations: added the model for 0-process. Extended version of the paper submitted to SYNT 201

Register-Bounded Synthesis

Traditional synthesis algorithms return, given a specification over finite sets of input and output Boolean variables, a finite-state transducer all whose computations satisfy the specification. Many real-life systems have an infinite state space. In particular, behaviors of systems with a finite control yet variables that range over infinite domains, are specified by automata with infinite alphabets. A register automaton has a finite set of registers, and its transitions are based on a comparison of the letters in the input with these stored in its registers. Unfortunately, reasoning about register automata is complex. In particular, the synthesis problem for specifications given by register automata, where the goal is to generate correct register transducers, is undecidable. We study the synthesis problem for systems with a bounded number of registers. Formally, the register-bounded realizability problem is to decide, given a specification register automaton A over infinite input and output alphabets and numbers k_s and k_e of registers, whether there is a system transducer T with at most k_s registers such that for all environment transducers T\u27 with at most k_e registers, the computation T|T\u27, generated by the interaction of T with T\u27, satisfies the specification A. The register-bounded synthesis problem is to construct such a transducer T, if exists. The bounded setting captures better real-life scenarios where bounds on the systems and/or its environment are known. In addition, the bounds are the key to new synthesis algorithms, and, as recently shown in [A. Khalimov et al., 2018], they lead to decidability. Our contributions include a stronger specification formalism (universal register parity automata), simpler algorithms, which enable a clean complexity analysis, a study of settings in which both the system and the environment are bounded, and a study of the theoretical aspects of the setting; in particular, the differences among a fixed, finite, and infinite number of registers, and the determinacy of the corresponding games

Church Synthesis on Register Automata over Linearly Ordered Data Domains

Register automata are finite automata equipped with a finite set of registers in which they can store data, i.e. elements from an unbounded or infinite alphabet. They provide a simple formalism to specify the behaviour of reactive systems operating over data ?-words. We study the synthesis problem for specifications given as register automata over a linearly ordered data domain (e.g. (?, ?) or (?, ?)), which allow for comparison of data with regards to the linear order. To that end, we extend the classical Church synthesis game to infinite alphabets: two players, Adam and Eve, alternately play some data, and Eve wins whenever their interaction complies with the specification, which is a language of ?-words over ordered data. Such games are however undecidable, even when the specification is recognised by a deterministic register automaton. This is in contrast with the equality case, where the problem is only undecidable for nondeterministic and universal specifications. Thus, we study one-sided Church games, where Eve instead operates over a finite alphabet, while Adam still manipulates data. We show they are determined, and deciding the existence of a winning strategy is in ExpTime, both for ? and ?. This follows from a study of constraint sequences, which abstract the behaviour of register automata, and allow us to reduce Church games to ?-regular games. Lastly, we apply these results to the transducer synthesis problem for input-driven register automata, where each output data is restricted to be the content of some register, and show that if there exists an implementation, then there exists one which is a register transducer

Parameterized Model Checking of Token-Passing Systems

We revisit the parameterized model checking problem for token-passing systems and specifications in indexed $\textsf{CTL}^\ast \backslash \textsf{X}$. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ in uni-directional token rings can be reduced to checking rings up to some \emph{cutoff} size. Clarke et al. (2004) have shown a similar result for general topologies and indexed $\textsf{LTL} \backslash \textsf{X}$, provided processes cannot choose the directions for sending or receiving the token. We unify and substantially extend these results by systematically exploring fragments of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ with respect to general topologies. For each fragment we establish whether a cutoff exists, and for some concrete topologies, such as rings, cliques and stars, we infer small cutoffs. Finally, we show that the problem becomes undecidable, and thus no cutoffs exist, if processes are allowed to choose the directions in which they send or from which they receive the token.Comment: We had to remove an appendix until the proofs and notations there is cleare

CTL* synthesis via LTL synthesis

We reduce synthesis for CTL* properties to synthesis for LTL. In the context of model checking this is impossible - CTL* is more expressive than LTL. Yet, in synthesis we have knowledge of the system structure and we can add new outputs. These outputs can be used to encode witnesses of the satisfaction of CTL* subformulas directly into the system. This way, we construct an LTL formula, over old and new outputs and original inputs, which is realisable if, and only if, the original CTL* formula is realisable. The CTL*-via-LTL synthesis approach preserves the problem complexity, although it might increase the minimal system size. We implemented the reduction, and evaluated the CTL*-via-LTL synthesiser on several examples.Comment: In Proceedings SYNT 2017, arXiv:1711.1022