Automata modulo theories

Symbolic automata better balances how automata are implemented in practice.

Wayeb: a Tool for Complex Event Forecasting

Complex Event Processing (CEP) systems have appeared in abundance during the last two decades. Their purpose is to detect in real–time interesting patterns upon a stream of events and to inform an analyst for the occurrence of such patterns in a timely manner. However, there is a lack of methods for forecasting when a pattern might occur before such an occurrence is actually detected by a CEP engine. We present Wayeb, a tool that attempts to address the issue of Complex Event Forecasting. Wayeb employs symbolic automata as a computational model for pattern detection and Markov chains for deriving a probabilistic description of a symbolic automaton.

Symbolic WS1S

We extend weak monadic second-order logic of one successor (WS1S) to symbolic alphabets byallowing character predicates to range over decidable first order theories and not just finite alphabets.We call this extension symbolic WS1S (s-WS1S). We then propose two decision procedures for such alogic: 1) we use symbolic automata to extend the classic reduction from WS1S to finite automata toour symbolic logic setting; 2) we show that every s-WS1S formula can be reduced to a WS1S formulathat preserves satisfiability, at the price of an exponential blow-up.

Effectively Monadic Predicates

Monadic predicates play a prominent role in many decidable cases, including decision procedures for symbolic automata. We are here interested in discovering whether a formula can be rewritten into a Boolean combination of monadic predicates. Our setting is quantifier-free formulas over a decidable background theory, such as arithmetic and we here develop a semi-decision procedure for extracting a monadic decomposition of a formula when it exists.