Nir Piterman

From Nondeterministic Büchi and Streett Automata to Deterministic Parity Automata

In this paper we revisit Safras determinization constructions for automata on infinite words. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Determinization is used in numerous applications, such as reasoning about tree automata, satisfiability of CTL*, and realizability and synthesis of logical specifications. The upper bounds for all these applications are reduced by using the smaller deterministic automata produced by our construction. In addition, the parity acceptance conditions allows to use more efficient algorithms (when compared to handling Rabin or Streett acceptance conditions).

Decoding the regulatory network of early blood development from single-cell gene expression measurements

Reconstruction of the molecular pathways controlling organ development has been hampered by a lack of methods to resolve embryonic progenitor cells. Here we describe a strategy to address this problem that combines gene expression profiling of large numbers of single cells with data analysis based on diffusion maps for dimensionality reduction and network synthesis from state transition graphs. Applying the approach to hematopoietic development in the mouse embryo, we map the progression of mesoderm toward blood using single-cell gene expression analysis of 3,934 cells with blood-forming potential captured at four time points between E7.0 and E8.5. Transitions between individual cellular states are then used as input to develop a single-cell network synthesis toolkit to generate a computationally executable transcriptional regulatory network model of blood development. Several model predictions concerning the roles of Sox and Hox factors are validated experimentally. Our results demonstrate that single-cell analysis of a developing organ coupled with computational approaches can reveal the transcriptional programs that underpin organogenesis.

Specify, Compile, Run: Hardware from PSL

We propose to use a formal specification language as a high-level hardware description language. Formal languages allow for compact, unambiguous representations and yield designs that are correct by construction. The idea of automatic synthesis from specifications is old, but used to be completely impractical. Recently, great strides towards efficient synthesis from specifications have been made. In this paper we extend these recent methods to generate compact circuits and we show their practicality by synthesizing a generalized buffer and an arbiter for ARMs AMBA AHB bus from specifications given in PSL. These are the first industrial examples that have been synthesized automatically from their specifications.

From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata

In this paper we revisit Safras determinization constructions. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Specifically, starting from a nondeterministic Buchi automaton with n states our construction yields a deterministic parity automaton with n²ⁿ⁺² states and index 2n (instead of a Rabin automaton with (12)ⁿn²ⁿ states and n pairs). Starting from a nondeterministic Streett automaton with n states and k pairs our construction yields a deterministic parity automaton with n^n(k+2)+2(k+1)^2n(K+1) states and index 2n(k+1) (instead of a Rabin automaton with (12)^n(k+1)n ^n(k+2)(k+1)^2n(k+1) states and n(k+1) pairs). The parity condition is much simpler than the Rabin condition. In applications such as solving games and emptiness of tree automata handling the Rabin condition involves an additional multiplier of n²n!(or(n(k+1))²(n(k+1))! in the case of Streett) which is saved using our construction

Predictive modeling of signaling crosstalk during C. elegans vulval development.

Caenorhabditis elegans vulval development provides an important paradigm for studying the process of cell fate determination and pattern formation during animal development. Although many genes controlling vulval cell fate specification have been identified, how they orchestrate themselves to generate a robust and invariant pattern of cell fates is not yet completely understood. Here, we have developed a dynamic computational model incorporating the current mechanistic understanding of gene interactions during this patterning process. A key feature of our model is the inclusion of multiple modes of crosstalk between the epidermal growth factor receptor (EGFR) and LIN-12/Notch signaling pathways, which together determine the fates of the six vulval precursor cells (VPCs). Computational analysis, using the model-checking technique, provides new biological insights into the regulatory network governing VPC fate specification and predicts novel negative feedback loops. In addition, our analysis shows that most mutations affecting vulval development lead to stable fate patterns in spite of variations in synchronicity between VPCs. Computational searches for the basis of this robustness show that a sequential activation of the EGFR-mediated inductive signaling and LIN-12 / Notch-mediated lateral signaling pathways is key to achieve a stable cell fate pattern. We demonstrate experimentally a time-delay between the activation of the inductive and lateral signaling pathways in wild-type animals and the loss of sequential signaling in mutants showing unstable fate patterns; thus, validating two key predictions provided by our modeling work. The insights gained by our modeling study further substantiate the usefulness of executing and analyzing mechanistic models to investigate complex biological behaviors.

Automatic Hardware Synthesis from Specifications: A Case Study

We propose to use a formal specification language as a high-level hardware description language. Formal languages allow for compact, unambiguous representations and yield designs that are correct by construction. The idea of automatic synthesis from specifications is old, but used to be completely impractical. Recently, great strides towards efficient synthesis from specifications have been made. In this paper we extend these recent methods to generate compact circuits and we show their practicality by synthesizing an arbiter for ARMs AMBA AHB bus and a generalized buffer from specifications given in PSL. These are the first industrial examples that have been synthesized automatically from their specifications

Enhanced Vacuity Detection in Linear Temporal Logic

One of the advantages of temporal-logic model-checking tools is their ability to accompany a negative answer to a correctness query with a counterexample to the satisfaction of the specification in the system. On the other hand, when the answer to the correctness query is positive, most model-checking tools provide no witness for the satisfaction of the specification. In the last few years there has been growing awareness of the importance of suspecting the system or the specification of containing an error also in cases where model checking succeeds. In particular, several works have recently focused on the detection of the vacuous satisfaction of temporal logic specifications. For example, when verifying a system with respect to the specification ϕ = G(req →Fgrant) (“every request is eventually followed by a grant”), we say that ϕ is satisfied vacuously in systems in which requests are never sent. Current works have focused on detecting vacuity with respect to subformula occurrences. In this work we investigate vacuity detection with respect to subformulas with multiple occurrences.

Faster Solutions of Rabin and Streett Games

In this paper we improve the complexity of solving Rabin and Streett games to approximately the square root of previous bounds. We introduce direct Rabin and Streett ranking that are a sound and complete way to characterize the winning sets in the respective games. By computing directly and explicitly the ranking we can solve such games in time O(mnk+1kk!) and space O(nk) for Rabin and O(nkk!) for Streett where n is the number of states, m the number of transitions, and k the number of pairs in the winning condition. In order to prove completeness of the ranking method we give a recursive fixpoint characterization of the winning regions in these games. We then show that by keeping intermediate values during the fixpoint evaluation, we can solve such games symbolically in time O(nk+1k!) and space O(nk+1k!). These results improve on the current bounds of O(mn2kk!) time in the case of direct (symbolic) solution or O(m(nk2k!)k) in the case of reduction to parity games

Synthesizing nonanomalous event-based controllers for liveness goals

We present SGR(1), a novel synthesis technique and methodological guidelines for automatically constructing event-based behavior models. Our approach works for an expressive subset of liveness properties, distinguishes between controlled and monitored actions, and differentiates system goals from environment assumptions. We show that assumptions must be modeled carefully in order to avoid synthesizing anomalous behavior models. We characterize nonanomalous models and propose assumption compatibility, a sufficient condition, as a methodological guideline.

Extended Temporal Logic Revisited

A key issue in the design of a model-checking tool is the choice of the formal language with which properties are specified. It is now recognized that a good language should extend linear temporal logic with the ability to specify all ω-regular properties. Also, designers, who are familiar with finite-state machines, prefer extensions based on automata than these based on fixed points or propositional quantification. Early extensions of linear temporal logic with automata use nondeterministic Buchi automata. Their drawback has been inability to refer to the past and the asymmetrical structure of nondeterministic automata. In this work we study an extension of linear temporal logic, called ETL2a, that uses two-way alternating automata as temporal connectives. Two-way automata can traverse the input word back and forth and they are exponentially more succinct than one-way automata. Alternating automata combine existential and universal branching and they are exponentially more succinct than nondeterministic automata. The rich structure of two-way alternating automata makes ETL2a a very powerful and convenient logic. We show that ETL2a formulas can be translated to nondeterministic Buchi automata with an exponential blow up. It follows that the satisfiability and model-checking problems for ETL2a are PSPACE-complete, as are the ones for LTL and its earlier extensions with automata. So, in spite of the succinctness of two-way and alternating automata, the advantages of ETL2a are obtained without a major increase in space complexity. The recent acceptance of alternating automata by the industry and the development of symbolic procedures for handling them make us optimistic about the practicality of ETL2a.